He said India had "set an example for the world in holding the largest democratic election in history".
The 36-day, nine-phase polls ended on Monday. The Election Commission said voter turnout was a record 66.38%.
The main contest is between the Congress and the main opposition BJP. Votes will be counted on 16 May.
"India has set an example for the world in holding the largest democratic election in history, a vibrant demonstration of our shared values of diversity and freedom," Mr Obama said in a statement.
"We look forward to the formation of a new government once election results are announced and to working closely with India's next administration to make the coming years equally transformative."
The election began on 7 April and has been held in nine phases for security and logistical reasons. With 814 million eligible voters, it is the world's biggest exercise in democracy.
A number of exit polls are suggesting that BJP leader Narendra Modi, the leader of India's main opposition BJP, is on course to win the general election.
The BJP dominated the campaign but analysts warn that exit polls have often been wrong in the past.
US President Barack Obama has congratulated India on its marathon general election and pledged to work closely with the next government.