Maxwell recently signed a contract that will cover the majority of the Blast season, which runs from May 20 until July 15, but he will miss the start of the campaign while playing for Royal Challengers Bangalore in India.
Stirling will play a handful of games for Warwickshire - under their T20 guise as Birmingham Bears - at the start of the season, with the exact number dependent on RCB's progress. Hasan Ali, the Pakistan seamer, is their other overseas player.
"We're very lucky to be able to call on somebody of Paul's calibre as cover," Mark Robinson, Warwickshire's coach said. "It's a short-term deal to cover what could be as little as one or up to three or four matches after the Blast Off.
"Paul made a big impact last season and the one over in which he hit five sixes and one four in an over will live long in the memory of Bears' fans. But he was also great to have in the Club and around the dressing room. He's a great lad with huge domestic and international experience."
Stirling set to miss England Test
Cricket Ireland announced on Tuesday that Stirling has been granted a No-Objection Certificate, which confirms he is highly unlikely to be involved in their Test against England at Lord's from June 1-4 - four days after the IPL final in Ahmedabad.
"It was a mutual discussion over more than one coffee," Malan said at the time. "It's all about... making sure that we find a balance between him playing for Ireland and then obviously some of his commitments he has around the leagues. This year, with a big white-ball focus in terms of a pinnacle event in the World Cup, we got to that agreement that, up until the World Cup, he will only play white-ball cricket for us."
Ireland will need to beat Bangladesh 3-0 in May and hope other results go their way in order to qualify automatically for that tournament, and are expecting to play in the qualifying tournament in Zimbabwe this summer. They will also play in the European Qualifier for the 2024 T20 World Cup in the United States, which will be staged in Scotland in July.