The Habibul Bashar-led team will play two Tests against England and a triangular one-day series also involving Australia.
The right-handed Indian opening batsman also emerged the leading run-scorer in the 16-team event with 349 runs.
Virat Kohli enters the three match ODI series against Bangladesh starting on Wednesday as the highest-ranked batsman on either side, in fourth place in the ICC rankings.
India picked up three Bangladesh wickets in the morning session after declaring their first innings on 462 for six but rain washed out the rest of the fourth day as the one-off Test headed for an inevitable draw in Fatullah, on Saturday.
Riding high on contrasting half-centuries from Shakib al Hasan and Mushfiqur Rahim, Bangladesh crushed Afghanistan by 105 runs in their opening Pool A match of the World Cup in Canberra.
Uncapped pace bowler Nazmul Hossain has been added to the Bangladesh squad for the second and final Test against India, starting on Friday in the port city of Chittagong.
Rain prevented a result at Oval during the ICC Champions Trophy match, in London, on Monday.
Corey Anderson smashed his first Test century as New Zealand reached 419 for eight against Bangladesh to take a first innings lead of 137 on the third day of the second and final Test in Dhaka on Wednesday.
South Africa lost both openers but were still 230 runs ahead of Bangladesh at the close on the third day of the first Test when bad light stopped play on Saturday.
New Zealand and Bangladesh enter their final group match of the ICC Champions Trophy, in Cardiff, on Friday, with the knowledge that even a win may not be enough to see either of them into the semi-finals.
Bangladesh shocked New Zealand by five wickets to keep their hopes alive of making it to the semi-finals at the ICC Champions Trophy in Cardiff, on Friday.
As far as Bangladesh were concerned, there was nothing worth mentioning except for a fifty each from captain Mushfiqur Rahim (59) and Shakib Al Hasan (52), the latter emerging as the Most Valuable Player (MVP) on account of his all-round showing in the series as he also claimed six wickets with his left-arm spin.
The third ODI between India and Bangladesh was called off after heavy showers rendered the ground unfit for play in Mirpur on Thursday.
Bangladesh registered a 23-run upset victory over defending champions Sri Lanka in a round robin league encounter to keep their hopes alive of qualifying for the final of Asia Cup T20 cricket tournament, in Mirpur, on Sunday.
Demoralised Bangladesh will look to end their campaign on a high when they face a rampaging New Zealand.
Bangladesh reached 245 for 6 in their second innings, a lead of 153, on the fourth day of the first Test.
Bangladesh defeated Pakistan by five wickets to qualify for the final of the Asia Cup.
Rohit Sharma smashed his fourth century of the World Cup as India beat Bangladesh by 28 runs to qualify for the semi-finals and eliminate their neighbours in the process.
Rohit Sharma stamped his class with an authoritative hundred in the company of magnificent Virat Kohli as India annihilated Bangladesh by nine wickets to set up a bumper summit showdown with arch-rivals Pakistan in the ICC Champions Trophy, in Birmingham, on Thursday.
War-torn Afghanistan, playing only their third match after being inducted as a Test-playing nation two years ago, completed a famous victory by defeating Bangladesh by 224 runs with 3.2 overs left on the final day on Monday.
Srinivas Bhogle and Purnendu Maji identify the Most Valuable Players of World Cup 2019.
With India needing 34 runs off the last two overs, Karthik hammered 29 not out off just eight deliveries, his third six sealing India's third, and the most hard-earned, victory over Bangladesh in the tournament.
Rohit Sharma roared back to form with a quickfire half-century, while Washington Sundar picked up three wickets as India outclassed Bangladesh by 17 runs to advance to the final of T20 tri-series, in Colombo, on Wednesday.
Bangladesh's first World Cup centurion Mahmudullah is hoping to extend his big scoring spree at the World Cup when he faces off against India.
Bangladesh outplayed Pakistan by 79 runs in the first one-day international in Dhaka on Friday, in only their second win over their rivals in 48 games across all three formats.
Rajneesh Gupta presents the interesting numbers from the match:
Australia survived a middle-order meltdown to beat Bangladesh by three wickets in a World Twenty20 Super 10 match on Monday to get their campaign up and running.
Srinivas Bhogle and Purnendu Maji identify the Most Valuable Players at World Cup 2019.
Hong Kong notched up a stunning two-wicket victory over Bangladesh in a thrilling qualifying round match but could not prevent the home side from booking a Super 10 berth in the World Twenty20 in Chittagong.
As far as the Indian team is concerned, even a 3-0 result against the hosts will not be enough for the second-placed side to claim the number one spot in the ICC rankings, while a favourable outcome for the home team will boost its qualifying chances for the 2017 ICC Champions Trophy.
Kumar Sangakkara continued his awesome batting form in Bangladesh as Sri Lanka won the second One-Day International by 61 runs in Dhaka on Thursday to take an unassailable 2-0 lead in the three-match series.
Bangladesh put in a disciplined performance in the field to restrict New Zealand to 145-8 in a World Twenty20 Super 10 stage match at the Eden Gardens on Saturday.
The confidence Kedar Jadhav has in his bowling comes from the fact that Mahendra Singh Dhoni used him as a surprise weapon during the ODI series at home against New Zealand last year.
Bangladesh captain Mashrafe Mortaza admitted that there will be pressure on his side ahead of their maiden semi-final appearance in a global event but quantum of expectation is manifold from India which has a huge cricket following.
Images from the ICC World Cup quarter-finals played between India and Bangladesh at the MCG on Thursday.
Spinner Rashid Khan celebrated his 20th birthday in style by producing a stunning all-round display as Afghanistan beat Bangladesh by 136 runs in an Asia Cup match in Abu Dhabi on Thursday.
India captain Virat Kohli, after a job well done against Bangladesh, said the players' hearts and minds are already on the big series against Australia.
Rajneesh Gupta salutes Tamim Iqbal's courage in the Asia Cup's opening game on Saturday and lists instances where cricketers braved injuries to battle it out for their teams.
Bangladesh opener Imrul Kayes hit an unbeaten half-century as the hosts took a lead of 128 with seven second-innings wickets remaining against England on the second day of the second and final Test in Dhaka, on Saturday.
India edged out Bangladesh by one run in a thrilling World Twenty20 match on Wednesday to keep alive their hopes of reaching the semi-finals.