Provided he passes a medical, Sangakkara will come straight to Warwickshire after the World Cup and replace Australian Martin Love, who had planned to join the county for the 2007 season before suffering a serious knee injury last weekend.
Warwickshire's Director of Coaching, Mark Greatbatch, said he was delighted to have secured the services of one the form players in world cricket.
"Kumar Sangakkara has had an outstanding 12 months and is ranked in the top 10 batsmen in the world in both forms of international cricket," Greatbatch said.
"He is looking forward to taking that sort of form into our domestic season."
Steyn will be available from the start of the season until June 3.
Greatbatch said: "We have a good crop of young bowlers at the club but we feel that Dale's extra pace can add something to our attack and hopefully help us to build some early season momentum."
Warwickshire are hoping that another South African, Paul Harris, who played for them in 2006, will rejoin the side after Steyn returns home in June, although that could be complicated by his recent elevation to the Proteas Test side.
That means he will now count as one of Warwickshire's two permitted overseas players, unlike last season when he was effectively classed as a 'home' players.
Warwickshire's chief executive, Colin Povey, said: "Paul's selection for South Africa over recent weeks posed a bit of a problem but provided we are able to juggle our resources within the new regulations regarding overseas players we are keen to have him back.
"Last summer he performed exceptionally well and his confidence is high after his international selection. We hope he will carry on where he left off last season."