The 34-year-old has played 25 Test matches and 26 one-day internationals for his country and joins the club as a Kolpak player on a short-term contract.
Best has a wealth of experience in all formats and averages 28 with the ball in 115 first-class matches.
Hampshire director of cricket, Giles White, said: ‘Fidel Edwards joined us last year under similar circumstances. He never looked back and this is a chance for Tino to emulate him.
‘He trained with us in Barbados during pre-season and looked good.
‘It has come about at short notice, initially on a short-term contract.
‘He seems excited about the opportunity and very motivated to do well.
‘We look forward to seeing how things develop.’
Hampshire’s current injury crisis includes fast-bowler Edwards, who suffered a fractured ankle at Headingley last week.
Meanwhile, fellow seamers Reece Topley, Gareth Berg and Ryan Stevenson are all currently not available for selection due to injury.
White added: ‘Unfortunately, Fidel has had a serious break and will have to undergo surgery tomorrow.
‘It’s a real shame for him, he has been unbelievable since he has been with us and has become an extremely popular member of the club.
‘We will support him through his recovery and look forward to having him back in a Hampshire shirt as soon as possible.
‘He is a class act and the team will miss him.’