The 26-year-old, who has made 237 professional appearances scoring 4,890 runs and taking 370 wickets, will join the Bears at the end of the 2022 domestic season.
Matthews, who is one of the leading all-rounders in world cricket, will assume the leadership role from Stafanie Taylor ahead of the next West Indies Women's Series, expected to be played later this year.
The all-rounder last played a Test match against Bangladesh in 2017 at Chattogram, the same year where he got his only Test century against India in Ranchi.
Stylish opener Laura Wolvaardt and experienced quick Ayabonga Khaka have been the big winners after dominant performances for the Proteas during their recent ODI series sweep over Ireland.
Rippon has been selected as part of a 15-player squad for the following three-game T20 series against Ireland in Belfast, two T20s and an ODI against Scotland in Edinburgh, as well as two T20s against the Netherlands in Amsterdam on August 4 and 6.
Kapp, ranked third in the world ODI all-rounder rankings, is one of three changes to the squad presently touring Ireland, with wicketkeeper Sinalo Jafta and opener Lizelle Lee also making a return.