Maxwell, who stood down from Australian duties in October saying he needed a break to deal with mental health issues, was named in both the one-day and Twenty20 squads to face the Proteas.
Selector Trevor Hohns said Maxwell had earned a recall with his performances captaining the Melbourne Stars in the Big Bash League (BBL), where he has scored 389 runs at an average of 43.22.
"It is fantastic to have Glenn back in both squads given his brilliant form in the middle order for the Stars along with his results with the ball," Hohns said.
Maxwell, 31, has played 110 one-dayers and 61 T20s for Australia, earning the nickname "Big Show" early in his career due to his match-turning abilities.
Wicketkeeper-batsman Matthew Wade and all-rounder Mitch Marsh, who last played limited-overs internationals in 2017 and 2018 respectively, were surprise inclusions on the back of strong BBL campaigns.
But Stoinis made neither the ODI or T20 squads, despite being named BBL player of the tournament with a competition-high 607 regular-season runs.
Hohns said Stoinis was on standby for South Africa, admitting the 30-year-old was unlucky to miss out.
"It is terrific to have a backup player of his calibre in such good form," he said.
Stoinis' last limited-overs international was Australia's World Cup semi-final loss against England last July, when he was dismissed for a two-ball duck.
Australia will play three T20s and three ODIs in South Africa, with the first fixture in Johannesburg on February 21.
Australia ODI squad
Aaron Finch (captain), Ashton Agar, Alex Carey, Pat Cummins, Josh Hazlewood, Marnus Labuschagne, Mitchell Marsh, Glenn Maxwell, Kane Richardson, Steve Smith, Mitchell Starc, Matthew Wade, David Warner, Adam Zampa.
Australia T20 squad
Aaron Finch (captain), Sean Abbott, Ashton Agar, Alex Carey, Pat Cummins, Mitchell Marsh, Glenn Maxwell, Jhye Richardson, Kane Richardson, Steve Smith, Mitchell Starc, Matthew Wade, David Warner, Adam Zampa.