Konrad, 38, swam the equivalent of 290 lengths of an Olympic-size swimming pool after his 36-foot boat, which was on auto pilot, drifted away from him off the South Florida coast.
The United States Coast Guard reported that friends became concerned when he failed to return for dinner.
After up to 12 hours in the water, he had treatment for hypothermia symptoms.
He played 82 games for the Dolphins between 1999-2004.

The 24-hour Underground service was originally scheduled for September, but was delayed over a dispute about pay and conditions.
Following the breakdown of talks on Wednesday, union leaders said the launch would not happen this year.
But during a trip to Japan Mr Johnson said: "We are going to have a Night Tube eventually."
He had previously said he was "relaxed" about when the service was introduced, as long as it happened before the end of autumn.
Mr Johnson said during a business visit to Japan: "We'll do a Night Tube and obviously I hope very much that the offer on the table, which is a very good one, is now communicated properly to the workforce of London Underground and I think we should just get on with it.
"We've done without it for 150 years and I'm sure we can rub along a little bit longe,r but we are going to have a Night Tube eventually."
Unions took industrial action during the summer having called for increased pay and a limit on how many all-night shifts their members would be asked to do.
As negotiations between the unions and London Underground came to a halt,  Finn Brennan from drivers' union Aslef, said discussions had broken up because LU management had "mishandled" the process.
Former Miami Dolphins running back Rob Konrad swam nine miles to shore after falling off his boat while fishing.
[NEXT_CONCEPT]
London mayor Boris Johnson has backed away from a timetable for the opening of the city's Night Tube.