He joins the Cherries from the Swedish side in a deal thought to be worth more than R30-million.
The 22-year-old has signed a four-year contract to join the newly promoted English Championship club, who had two previous bids rejected.
Despite their desire to keep hold of Rantie, Malmo were forced to accept the third offer as the Cherries smashed their previous record signing.
His move is still subject to a work permit being granted and international clearance, although it is not anticipated there will be any issues for a player who has become a Bafana regular under Gordon Igesund.
“AFC Bournemouth has agreed a deal to take South African international striker Tokelo Rantie to the Goldsands Stadium,” read a statement on the cub's website this afternoon.
“The Cherries fought off interest from a host of other clubs to secure the signing of the forward, who only joined Champions League chasers Malmo permanently in April having impressed whilst on loan from Orlando Pirates.
“Rantie will not feature in tonight’s Capital One Cup tie at Watford, and will link up with the squad later this week.”