The surgery will be performed by the New York Mets' team physician, Dr. David Altchek, according to the source.
Nathan, who felt discomfort in his elbow during a March 6 outing against the Boston Red Sox, made the decision to have surgery after playing catch with Twins pitching coach Rick Anderson for 10 minutes on Sunday.
On Sunday, Nathan said he sought opinions from a number of players, including teammate Carl Pavano, who had the same surgery performed by Altchek.
"He knows Altchek very well and had nothing but great things to say about him," Nathan said Sunday. "The guy is very personable, very easy to talk to, which is important."
Nathan said he was surprised at how many players had reached out when word spread he was facing possible surgery. He said New York Yankees closer Mariano Rivera had asked for his phone number, though the two hadn't spoken as of Sunday.
Nathan said his goal is to make it back for Opening Day of 2011. Tommy John surgery usually has a recovery of a year or more.
The 35-year-old right-hander signed a $47 million contract two years ago that guarantees him $11.25 million both this season and next. The Twins have a $12.5 million option for 2012, with a $2 million buyout.
Nathan went 2-2 with a 2.10 ERA and a career-best 47 saves last season.
Amy K. Nelson is a writer for ESPN The Magazine. Information from The Associated Press was used in this report.