Nathan, who leads the major leagues with 246 saves since 2004, made the decision after playing catch with Twins pitching coach Rick Anderson for 10 minutes on Sunday.
"It didn't go like we hoped," Nathan said. "We knew it was a longshot, but I think this will clear my head. There definitely was no gray area. It was definitely on the dark side. We know now that we're going to need to go in and have some surgery done and get this thing taken care of."
Nathan hopes to have Tommy John surgery within two weeks to repair the torn ulnar collateral ligament in his right elbow. He was injured on March 6 during a 20-pitch outing in a spring training game against the Boston Red Sox.
"The one thing we didn't want to do was work on this for two or three months and then have the surgery," general manager Bill Smith said.
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 has set his sights on returning at the start of the 2011 season.
"I'm very confident," he said. "I've talked to the doctors. The percentages of coming back are very good. You never want to say 100 percent, but it's pretty close to being 100 percent of the time."
Nathan went 2-2 with a 2.10 ERA and a career-best 47 saves last season.
The in-house relievers likely to replace Nathan include Jon Rauch, who has 26 big league saves, the most of any Twins pitcher besides Nathan. Other possible candidates are Matt Guerrier, Jesse Crain, Jose Mijares and Pat Neshek.
"You can't just name a guy closer if he's not willing to be a closer. So you have to talk to people," manager Ron Gardenhire said. "We know that probably everybody out there would say, 'Yes, I'd like to be the closer.' But if that guy's not really comfortable doing that, we want to give it a little more time. Then we will make the decision."
Rauch appears to be the most prepared for the role.
"He's got all the closing stuff: punchout pitches, the whole package," Gardenhire said. "Whether he wants to do that or not or whether it's the right thing to do remains to be seen."
The Twins could also try to trade for a proven closer.
"We may have the best option in-house, but we're going to consider everything," Smith said, adding: "Nothing has to be set for the entire season on April 5. We're going to look at what we have available. Obviously, we'll weigh what we have to give up in any trade as we do all year round."
Since hurting the elbow two weeks ago, Nathan had tried strengthening the muscles around the joint, hoping to pitch through the injury. But the throwing session confirmed his worst-case scenario.
"It started out well," Nathan said. "Everything felt good at the beginning. I didn't want to go super intense but enough to where it was along the lines of playing a normal game of catch.
"I got out to about 60 or 70 feet and started feeling a little bit of stiffness. I wasn't sure if it was from the forearm or from the elbow. I just kept throwing, and it became clear that it was an injured elbow. It was getting harder and harder. It became clear that it didn't feel good. I don't have a number on what I threw, but it wasn't very long. It was probably only a few minutes of playing catch when I started feeling stiff."
Nathan said he would rehabilitate from the surgery in Minnesota.
"I think it will help me get through this thing and at least be a part of the team a little bit," he said. "I'm very comfortable in Minnesota. We have a house there, and my family would like it. Obviously, I would like to help out whoever is thrown into that role."
He'll be missed by his teammates, though they're optimistic someone will step forward and succeed.
"We didn't know if Joe Nathan was going to be able to do what Joe Nathan has done over the last six years," right fielder Michael Cuddyer said. "Who knows what's in store for us now? Maybe it opens up a door or an opportunity for whoever it may be to step in."