The 31-year-old, whose current deal expires in June, is understood to be the Baggies’ highest earner.
And now the former England man is set to start a new chapter in his career in the United States with Inter Miami.
The MLS side are owned by Beckham and managed by former Manchester United midfielder Phil Neville.
According to reports, both New York Red Bulls and DC United also expressed an interest in signing Gibbs this summer.
But the defender has decided to join Miami.
The MLS side officially kick-off their season next month.
Gibbs, though, will remain with Albion for the remainder of the 2020/21 campaign before moving to Inter midway through their season.
The full-back joined Albion for £7million in 2017 from boyhood club Arsenal.
In total he has made more than 100 appearances for the club.
But over the last two years, he has been blighted by injuries and has now lost his place in the starting XI to Conor Townsend.
Townsend signed a new three-year contract at The Hawthorns last month.
And it is believed both Albion and Gibbs feel the time is right for a parting of the ways – with the left-back understood to have agreed terms of a two-and-a-half year deal with Miami.
Alongside signing Gibbs, the Beckham-owned franchise recently swooped to bring in former Stoke defender Ryan Shawcross.
Beckham has also made it clear he would like to sign either Cristiano Ronaldo, Lionel Messi or Neymar one day.
A statement released by Albion said: “Albion left-back Kieran Gibbs will join MLS side Inter Miami when his Hawthorns contract expires this summer.
“The 31-year-old will remain with the Baggies for the duration of the 2020/21 Premier League season.
“Gibbs joined Albion from Arsenal in August 2017 and has to date made 100 appearances for the club, scoring five goals.
“The club wishes Gibbo well with his summer move to the United States and all the very best in the future.”
Gibbs’ departure means Albion are likely to enter the market for a new left-back this summer – with that player set to compete with Townsend for a starting spot.
Meanwhile, Albion have extend their accounting year for 2020 from June 30 to July 31.
It means the accounts will now include the whole of their promotion winning season from the Championship.
That extension means their likely to be delay as to when the accounts are published.