Salah had been a rumoured January transfer target for Brendan Rodgers' Liverpool, although they were usurped by Chelsea's bid rumoured to be in the region of £18 million.
And Mourinho confirmed ahead of his side's FA Cup tie at home to Stoke City on Sunday that a deal will be finalised imminently, after a fee was agreed with the Swiss club on Thursday.
The 21-year-old has come to prominence with a series of impressive displays against the Premier League club in recent seasons, having scored against them in European competition last season and this.
His arrival at Stamford Bridge goes some way to off-setting the departure of Juan Mata - who completed a £37.1m move to Manchester United on Saturday.
Salah, who has scored 17 goals in 27 games for Egypt, may be in line to make his Chelsea bow when Mourinho's side welcome West Ham to Stamford Bridge on Wednesday.
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