The golfer has finally found happiness with his girlfriend of four years

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Things have been going well for Tiger Woods and his longtime girlfriend, Erica Herman — and those close to him say that the pair's relationship is getting even more serious.

"They live together at his house now," a source close to the golfer tells PEOPLE in this week's issue, referring to the mansion that Woods owns in Jupiter, Florida.

According to the source, Woods' two kids — Charlie, 11, and 13-year-old daughter Sam — are also encouraging of the relationship. "The kids like her," the source tells PEOPLE.

Woods and Herman have been dating for nearly four years. They were first pictured together at the Presidents Cup in New Jersey in September 2017. It was there at the tournament — where Woods served as an assistant captain for the United States team — that Herman wore a badge reserved for the girlfriends and wives of players.

For more on Woods and the latest developments in his life and career, pick up this week's issue of PEOPLE, on stands Friday.

Since then, the couple has only grown closer, with Herman also by his side as he won the 2019 Masters. Herman, a former restaurant manager, is now focusing on building a home with Woods.

According to the source, Herman also gets along well with Elin Nordegren, Woods' ex-wife. "Elin has a friendly relationship with Erica," the source says. "Tiger has come a long way and Elin acknowledges that. She is happy that he is dating Erica."

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Woods and Nordegren divorced in 2010 after a sex scandal rocked their marriage.

"Elin put her own feelings aside to make sure the kids have a great relationship with their dad," the source says. "They do a great job of co-parenting."

This week, Woods' team announced that the golfer had undergone yet another back surgery, this time "a microdiscectomy procedure to remove a pressurized disc fragment that was pinching his nerve after experiencing discomfort following the PNC Championship."

A message shared on Woods' Twitter said doctors believe the operation was a success and "expect him to make a full recovery."