Lindholm, 22, has been looking for closer to $5.5 million per season as late as last week, but came down to Anaheim's final offer.
Lindholm, picked sixth overall in the 2012 draft by Anaheim, has 92 points in 236 NHL games and led the Ducks with a career-high 115 blocked shots last season.
The Swede missed training camp and the first eight regular-season games this fall while holding out.
"I'm really happy to be back in Anaheim,'' Lindholm said in a phone interview from Sweden. "That's where I've been all my career. This is the only time when we had time to sign me, and we could still keep some players. It was kind of perfect that way to keep the team that we had last year.''
General manager Bob Murray echoed Lindholm's excitement about the deal, which allows the Ducks to preserve the four-time Pacific Division champions' core. A dominant regular-season team, Anaheim has won only three playoff rounds in the past four seasons, never advancing past the Western Conference finals.
"He's part of the future of this franchise, and we did everything we could to get him signed at a fair price,'' Murray said. "I wanted to give this group another shot, and I'm going to do everything in my power to keep it that way.''
Lindholm agreed to slightly less than the six-year, $32.4 million deal signed by Buffalo defenseman Rasmus Ristolainen earlier this month. Winnipeg's Jacob Trouba is the NHL's only remaining restricted free agent without a deal, and he has asked for a trade.
"I was hoping to get this done in the summer, of course, but that's just how it is,'' Lindholm said. "I can't do too much about that.''
Lindholm has been working out daily at home with a Swedish Elite League team, along with extra work at home. He expects to be ready to step into Anaheim's lineup after he gets his visa, although that process could take up to two weeks.
"I've been practicing hard,'' Lindholm said. "It's going to be exciting to come back and play some real hockey again.''
Forward Rickard Rakell, Lindholm's teammate and fellow Swede, ended his own holdout by agreeing to a six-year, $22.8 million deal with Anaheim on Oct. 14, but he didn't practice with the Ducks until Wednesday.
There has been much speculation that the Ducks might have to trade away a player now to manage their salary-cap space, but putting defenseman Simon Despres on long-term injured reserve has bought them some wiggle room for the moment. Despres left the season opener at Dallas with an unspecified upper-body injury.
Lindholm repeatedly mentioned the importance of getting a deal that would allow the Ducks to keep their core together. The Ducks were widely expected to afford Lindholm by trading another defenseman -- most likely Cam Fowler, the U.S. Olympian and a regular on Anaheim's defense for six years.
Fowler is the Ducks' second-leading scorer this season with three goals and four assists in eight games. He is also leading the Ducks in ice time, averaging nearly 24 1/2 minutes per game.
The Associated Press contributed to this report.