Rantie has 12 caps for South Africa and had also been linked with Celtic and Middlesbrough, but he will join Bournemouth on a four-year contract, subject to international clearance and a work permit.
The fee for Rantie is undisclosed, although Sky sources understand that Bournemouth are to pay not far short of £2.5m for his services.
Rantie, who originally joined Malmo on loan from Orlando Pirates before signing a permanent deal in April this year, will link up with his new team-mates later this week.
Bournemouth were promoted into the Championship last season and have won two of their first four games in the second tier.
However, they have also been on the wrong end of a pair of heavy defeats, losing 6-1 to Watford and 5-1 to Huddersfield.