The award will be presented as such for the first time at the annual ICC Awards ceremony in London on Wednesday.
Sobers, who was knighted for his services to cricket in 1975, said: "It is a great honour to have this award named after me."
"I have been fortunate to enjoy a long association with a game that I and millions of others around the world cherish, and I appreciate this honour which has been initiated on my behalf, and I wish all those players who have been nominated as Player of the Year the very best of luck."
ICC president Ehsan Mani said that naming the Player of the Year award after Sobers would add strong meaning for the individual voted as the game's most outstanding player of the past 12 months.
"The ICC is delighted that Sir Garfield Sobers has accepted its invitation to have this perpetual trophy named in his honour," said Mr Mani.
"Sir Garfield Sobers was an outstanding all-rounder, a wonderful ambassador, and a man who has inspired generations of cricketers to play the game with flair and passion.
"It is fitting that we name the Player of the Year award - international cricket's highest individual honour - after this legend of the sport.
The recommendation to name the award after Sobers came from a group of three cricket legends - Richie Benaud, Sunil Gavaskar and Michael Holding - who were asked by the ICC to select an individual with whom to honour cricket's ultimate individual award.
Sobers played 93 Tests and one One-Day International in his 20-year career, scoring 8032 runs and claiming 235 wickets in Test cricket.