We have no solid information on when President Matthew Ellis was elected.
However, we do know that he was President in 2013, when Iron Man 3 was set.
Additionally, thanks to a quote in in Captain America: The Winter Soldier found in the Smithsonian that reads "Welcome back, Cap" by President Ellis, we can assume that he was President at the time of Steve Rogers' defrosting in 2011.
If we assume that the elections in the Marvel Cinematic Universe follow real world dates, that would mean that in order for Matthew Ellis to be in office for both of these events, he would have had to have been elected in the 2008 election, and then re-elected for his second term in the 2012 election. Logically, that means that after 2016 we should be seeing a new President in the Marvel Cinematic Universe.
Edit: As of the Agents of SHIELD season 3 episode "Bouncing Back", we know that Matthew Ellis is still the President of the United States in March 2016.