In the meeting, the two leaders assured the nation of a peaceful transition of power on January 20 next year.
Biden would also travel to Jordan for a summit meeting with the heads of States of Jordan, Egypt and the president of Palestinian Authority.
In Amman, Biden will meet with King Abdullah of Jordan, Egyptian President Abdel Fattah El-Sisi, and Palestinian Authority President Mahmoud Abbas.
Biden's statement announcing Jha's appointment praised him as one of the leading public health experts in America and "a well known figure to many Americans from his wise and calming public presence."
The US on Monday announced a new international travel system under which fully vaccinated individuals would be allowed to enter the country beginning in November.
Dr Anthony Fauci has been named as Chief Medical Adviser to the President on COVID-19, while Dr Rochelle Walensky has been named as Director of the Centers for Disease Control and Prevention; and Dr. Marcella Nunez-Smith as COVID-19 Equity Task Force Chair.
Observing that amazing things have happened over the last 10 years, the former US President Barack Obama on Friday said that all this could be accomplished because of the hope and believe that his country had in him.