"It is clear Shane's retirement from the international game is a monumental loss to world cricket," Bransgrove told the English county's official Web site (www.hampshirecricket.com) on Thursday.
"At the same time it is fantastic for Hampshire cricket and our supporters he has chosen to see out his playing career at the Rose Bowl."
Warne, 37, told a packed news conference in Melbourne on Thursday he would retire from international cricket after the final Ashes Test against England next month.
He said he was quitting to spend more time with his children and to pursue a new career, possibly as a commentator.
"I'm going to retire at the end of the Sydney Test match," he said. "It's been an unbelievable journey...but my time is now."
Warne, who retired from one-day internationals in 2003, is the world's leading Test wicket-taker (699) and arguably the most famous cricketer since his compatriot Don Bradman.
He intends to honour the final two seasons of his contract with Hampshire.
"Shane has been a cornerstone of the restructuring of Hampshire cricket over recent years that has seen the team develop into an attractive and seriously competitive unit," said Bransgrove.
"I never doubted his intentions to fulfil his contract with Hampshire and I know I speak for all Hampshire fans when I congratulate him on his achievements to date and look forward to seeing him back at the Rose Bowl next year."
Under his captaincy, Hampshire have twice finished runners-up in the county championship.