There's actually a group of economists that gets together and decides, officially, whether the U.S. is in a recession. And that group just decided it's too soon to say whether the recession has ended.
The NBER's Business Cycle Dating Committee says:
Although most indicators have turned up, the committee decided that the determination of the trough date on the basis of current data would be premature. Many indicators are quite preliminary at this time and will be revised in coming months.
A "trough date" is the moment when the economy stops falling and starts climbing again. So what the NBER is saying is the recession may be over, but they can't say for sure.
Our colleagues over at The Two Way are putting the question to a popular vote:
Here's more on the question from the AP and the New York Times.