Tiger Woods said Brooks Koepka's return to the PGA Tour makes it "a better place to play" and is a "win for everyone".
Five-time major winner Koepka quit LIV Golf with a year of his contract remaining, stating he wanted to spend more time with his family.
The 35-year-old subsequently applied for his PGA Tour membership to be reinstated, with both his availability and high profile effectively causing officials to rewrite their own rules by instigating a Returning Member Programme.
As part of his return, Koepka has agreed to stringent restrictions on his financial benefits as well as a charitable donation of $5m (ÂŁ3.71m), and is set to feature at the upcoming Farmers Insurance Open, live on Your Site from January 29.
Woods, who is on the PGA Tour board, feels the outcome was the best for all concerned.
"There are opinions from both sides, we are not going to satisfy everyone," said 15-time major winner Woods.
"We know that, but the whole idea is to make our tour better than what it was. With Brooks' addition to the [PGA] Tour, it does. It makes it a better place to play.
"Now with players who have earned equity, and there are four more years of potential earning of equity for these players, the fact that they own the [PGA] Tour, if Brooks plays, it puts more money in their pocket. It is a win for everyone."
Woods believes the presence of Koepka will provide a welcome "additive" to the PGA Tour fields.
"Having another world-class player that these guys are going to try and beat, that is what the fans demanded, that is what the fans wanted for our fan initiative program, and I think we have addressed that," he said.
Bryson DeChambeau, though, has ruled out following Koepka in making a swift return to the PGA Tour.
Speaking at the LIV Golf captains' press conference, the American said: "I'm contracted through 2026, so I'm excited about this year."
On Koepka's departure, DeChambeau added: "I had no idea that would happen. No idea what the penalties would even be.
"Right now I've got a contract. I'm looking forward to seeing what we can do at LIV Golf this year."
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