Baker also joined Hampshire from Somerset at the end of last summer and has taken two five-wicket hauls in six County Championship matches this season.
The Hundred was his breakout tournament, however. He took a hat-trick against Brook’s Northern Superchargers in addition to his spells against Spirit and Fire.
Troubled by back injuries earlier in his career, Baker revealed to BBC Sport after he was called into the England white-ball squad that he drinks “bone broth” every day to help guard against further problems.
“He’s got me out before, a few years ago in The Hundred,” Brook added.
“He can swing it both ways with exceptional death skills as well so to have him in the team and for him to be opening up tomorrow is awesome.”
The series against South Africa are Brook’s second since being appointed full-time white-ball captain earlier this year.
England won all six matches against West Indies – three ODIs and three T20s – under Brook earlier in the summer.
With the Ashes set to take the focus this winter, England are in the early stages of building towards the 2027 50-over World Cup, after three disappointing global events in a row.
There is also a T20 World Cup in India and Sri Lanka in February next year.
“We’re trying to create an environment where we’re working towards something, like [World Cup-winning captain Eoin Morgan] Morgs did when he took over years ago,” Brook said.
“South Africa play their cricket slightly different to West Indies.
“We have got to assess situations slightly quicker against a team like this. They are a more conventional side.”
The Proteas arrive in the UK, having won an ODI series in Australia 2-1 eight days ago. They thrashed England by seven wickets at the Champions Trophy in March – a match that proved to be Jos Buttler’s last as captain.
Bowler Kagiso Rabada is in their squad but will miss the first ODI as his workload is managed.
David Miller and Donovan Ferreira, who both impressed in The Hundred, are in the T20 squad only.
Ferreira’s omission is a tactical choice while captain Temba Bavuma confirmed Miller remains part of South Africa’s ODI plans but was not available for this series because his Hundred commitments clashed with their build-up.