Wales international Bale confirmed in a video posted on social media that he will join MLS side LAFC when his Real Madrid contract expires later this week.
The 32 year-old had also been linked with Madrid-based Getafe, which he categorically ruled out, as well as former side Tottenham and hometown club Cardiff among others.
Bale is reported to have held talks with Cardiff boss Steve Morison during a recent trip to the club's training base, which it shares with the Wales national side.
Cardiff owner Tan has confirmed the Welsh side was in for the forward, but it was unable to match the terms offered by LAFC – even if money was not the decisive factor.
"We were very, very keen and of course it would have been a big coup for us and would have been great for Gareth Bale to play for his hometown," Tan said. "We tried our very best, but we failed. Everybody would be happy if Gareth Bale returned home and played in Cardiff, but unfortunately the offer was too attractive to turn down.
"He actually originally wanted to come, money wasn't the matter. We still tried to come up with a good offer for him.
"But finally we had to compete when there is a lot of big American advertisers. The commercial deals there were very good, the commercial deal was very good for Gareth Bale."
Bale is to join LAFC on a year-long contract using targeted allocation money, taking him through until the World Cup, where Wales will compete after a 64-year absence.
The Southampton academy product reportedly has the option to stay on for the 2023 season, but Tan has not ruled out a switch to Cardiff next year to see out his career.
"His contract is for 12 months. We will see what happens. Maybe in 12 months Gareth will want to come back and come home, serve Cardiff, his hometown," Tan said. "He has never played in Cardiff, a club he and his family are fans of. Hopefully in 12 months, he's still young, he will come back at 35 and some play until they are 40 years old.
"He's still got a few years and hopefully he will come and play for Cardiff. It wasn’t really about the money. Gareth wanted to help Cardiff and help Wales.
"It wasn't really the money – that's why we could negotiate with him. He tried his best, but I think the offer from LAFC is too big to turn down."
Bale's signing boosts an LAFC side that already lead the Supporters' Shield race and also secured Giorgio Chiellini ahead of the MLS transfer window opening next month.
The pair could therefore make their debuts in El Trafico against rivals LA Galaxy on 8 July.