Other big names who were sworn-in as cabinet ministers are Rajnath Singh -- who retains home ministry -- Nitin Gadkari, Nirmala Sitharaman and Smriti Irani.
Sushma Swaraj opted out of the government.
Former foreign secretary S Jaishankar also included in the cabinet as a surprise pick.
J P Nadda may succeed Amit Shah as BJP president.
JD-U stayed out of the government reportedly due to differences over the number of ministerial berths offered.
Narendra Modi was on Thursday sworn in as the Prime Minister for a second term helming a 58-member ministry with Bharatiya Janata Party chief Amit Shah making his debut at the Centre and former foreign secretary S Jaishankar emerging as a surprise pick while party veteran Sushma Swaraj was among the outgoing ministers who found no place.
Wearing a beige Nehru jacket, Modi, 68, was administered the oath of office and secrecy by President Ram Nath Kovind at a glittering ceremony just before sunset at the forecourt of majestic Rashtrapati Bhavan, capping a landslide win for the BJP which won 303 of the 542 seats.
Besides 25 Cabinet ministers including Modi, Shah, Rajnath Singh, Nirmala Sitharaman, Nitin Gadkari, Smriti Irani, Piyush Goyal and Jaishankar, nine were sworn in as Minister of State with Independent charge and another 24 as Minister of State.
'Honoured to serve India!' tweeted Modi after taking the oath.
Besides Swaraj, who did not contest the elections on health grounds, eight-time MP Maneka Gandhi, six-time MP Radhamohan Singh, Mahesh Sharma, Jayant Sinha, Jual Oram, Ram Kripal Yadav, Rajyavardhan Singh Rathore, all of BJP, and Anupriya Patel (of BJP ally Apna Dal) failed to make the cut despite winning their respective seats.
Anantkumar Hegde, a Hindutva leader from Karnataka who is known for his controversial statements, was also dropped.
Suresh Prabhu and J P Nadda (both Rajya Sabha) also did not find a place. Speculation is rife that Nadda, who was made BJP's UP in-charge, may succeed Shah.
Arun Jaitley, who held the Finance portfolio, had already opted out of the government for health reasons.
Union minister Hardeep Singh Puri, a former diplomat who lost the elections, managed to retain his berth. Jaishankar and Puri will have to enter Parliament within 6 months and they could take the Rajya Sabha route.
Portfolios for the news ministers were not announced amid reports that Shah may get the finance portfolio and Rajnath retaining Home.
Key BJP ally Janata Dal-United stayed out of the government in what appears to be a sign of differences with the saffron party over the number of ministerial berths offered to the party.
"We are not joining the government. This is our decision," Pavan Varma, who is also the general secretary of the Janata Dal (United), told PTI. The JD(U), will, however remain part of the NDA.
Smriti Irani, who earned the tag of giant killer for defeating Congress chief Rahul Gandhi in his home turf in Amethi in Uttar Pradesh, was among the six women ministers.
While the inclusion of Shah, seen as BJP's key strategist who helped the party expand its base after taking over the reins of the party in 2014, was the subject of intense speculation since the party's spectacular victory on May 23, Jaishankar, considered close to Modi, was a surprise pick.
A seasoned diplomat, Jaishankar, was the Indian government's pointsman for China and the US.
Son of late K Subrahmanyam, one of India's leading strategic analysts, Jaishankar was a key member of the Indian team which negotiated the landmark Indo-US nuclear deal.
Jaishankar retired from the Indian Foreign Service only last year to join Tata Trusts.
Uttar Pradesh accounted for a maximum of 9 ministers while states like West Bengal where the BJP had a spectacular showing winning 18 seats accounted for two ministers--Babul Supriyo and Debasree Chaudhuri. Kerala, where the BJP drew a blank, had a token representation in V Muraleedharan, the Rajya Sabha MP from Maharashtra.
As the sun set over the Rashtrapati Bhavan, the two-hour swearing-in ceremony commenced with 8,000 people packing into the forecourt of the historic British-era presidential palace.
In a grand ceremony with overtones of a US presidential inauguration, heads of state and government, chief ministers, India Inc honchos, opposition leaders, BJP members and showbiz stars rubbed shoulders as they watched President Kovind administer the oath of office.
Former prime minister Manmohan Singh, Congress president Rahul Gandhi and United Progressive Alliance Chairperson Sonia Gandhi were among those who were present.
The two-hour ceremony is the largest event to be held in Rashtrapati Bhavan, officials said.
D V Sadananda Gowda, Narendra Singh Tomar, Ravi Shankar Prasad, Thanwar Chand Gehlot, Ramesh Pokhriyal, Arjun Munda, Harsh Vardhan, Prakash Javadekar, Dharmendra Pradhan, Mukhtar Abbas Naqvi, Pralhad Joshi, Mahendra Nath Pandey, Giriraj Singh and Gajendra Shekhawat were the other BJP leaders who were made cabinet ministers.
Harsimrat Kaur Badal, Arvind Sawant, and Ram Vilas Paswan represented allies Akali Dal, Shiv Sena and Lok Janshakti Party respectively.
The nine who took oath as minister of state with independent charge are -- Santosh Kumar Gangwar, Rao Inderjit Singh, Shripad Yesso Naik, Jitendra Singh, Kiren Rijiju, Prahalad Singh Patel, Raj Kumar Singh, Hardeep Singh Puri and Mansukh L Mandaviya.
The 24 ministers of state were --Faggan Singh Kulaste, Ashwini Kumar Choubey, Arjun Ram Meghwal, V K Singh, Krishan Pal, Danve Raosaheb Dadarao, G Kishan Reddy, Parshottam Rupala, Ramdas Athawale, Sadhvi Niranjan Jyoti, Babul Supriyo, Sanjeev Kumar Balyan, Dhotre Sanjay Shamrao, Anurag Singh Thakur, Angadi Suresh Channabasappa, Nityanand Rai, Rattan Lal Kataria, V Muraleedharan, Renuka Singh Saruta, Som Parkash, Rameswar Teli, Pratap Chandra Sarangi, Kailash Choudhary, Debasree Chaudhuri.
With Modi pledging 'sabka saath, sabka vikas and sabka vishwas' mantra, Naqvi, the cabinet's lone Muslim face, will have the responsibility of winning the hearts of minorities and taking forward the 'development without appeasement' policy.
Modi can have as many as 80 ministers in the 543-member Lok Sabha.
As per the Constitution, the total number of Union ministers, including the Prime Minister shall not exceed 15 per cent of the number of members in the LS.
This is the second time Modi took the oath at the forecourt of Rashtrapati Bhavan.
Modi was sworn in by the then President Pranab Mukherjee in 2014 in the presence of over 3,500 guests including the heads of South Asian Association for Regional Cooperation countries.
Earlier, Chandra Shekhar in 1990 and Atal Bihari Vajpayee in 1999 were sworn in at the sprawling forecourt.
Leaders of BIMSTEC (Bay of Bengal Initiative for Multi-Sectoral Technical and Economic Cooperation) countries including President of Bangladesh Abdul Hamid, Sri Lankan President Maithripala Sirisena, Nepal Prime Minister K P Sharma Oli, President of Myanmar U Win Myint and Bhutanese Prime Minister Lotay Tshering also attended the gala event.
From Thailand, its Special Envoy Grisada Boonrach represented the country.
Besides India, BIMSTEC comprises Bangladesh, Myanmar, Sri Lanka, Thailand, Nepal and Bhutan as members.
Kyrgyz President and current chair of Shanghai Cooperation Organisation Kyrgyz President Sooronbay Jeenbekov, and Mauritius PM Pravind Kumar Jugnauth also attended.