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Hampshire have been in discussions with Afridi's agent ever since the Blast's fixtures were confirmed, and have confirmed his availability for their seven remaining group games, plus the knockout stages should they qualify.
Hampshire won their first game in the competition on Monday against Essex, and Afridi will debut against Surrey at The Oval on Thursday evening.
Unlike Afridi, Wasim had never officially signed for Nottinghamshire this season, but did play seven Blast games for them last year, taking 10 wickets - including the crucial scalp of AB de Villiers in the quarter-final win against Middlesex - and conceding just 6.64 runs per over. They have won two of their first three games - the other was washed out - in this year's Blast, despite the absence of Harry Gurney through injury.
Wasim has gone straight into the squad to play second-placed Lancashire at Liverpool on Tuesday afternoon, meaning he could play two T20s in the space of 24 hours after appearing in the third T20I against England on Monday night.
Azam is set to play seven group-stage games for Somerset this season, plus the knockouts if they qualify, after topping the run charts last year. His first game will be Somerset's televised game against Worcestershire at Edgbaston on Wednesday.