The 21-year-old has come to prominence with a series of impressive displays for the Swiss Super League champions, including scoring against Chelsea in last season's UEFA Europa semi-finals, though Basel exited the competition 5-2 on aggregate.
He followed that with a strike against the London club in a 2-1 win at Stamford Bridge in this year's UEFA Champions League in September.
Salah has been a rumoured transfer target for Brendan Rodgers' Liverpool side during the January transfer window, although they have been usurped.
A statement on the club's official website read: "Chelsea Football Club can confirm an agreement has been reached with FC Basel for the transfer of their 21-year-old attacking midfielder Mohamed Salah.
"The move is subject to the Egyptian international agreeing personal terms and completing a medical examination."
Basel also confirmed the agreement, and said the announcement was to "prevent further speculation".
"To prevent further speculation, Chelsea FC and FC Basel 1893 announce that the two clubs have agreed on Wednesday night in London on the immediate transfer of Mohamed Salah," read a Basel statement.
"The completion of the transfer is subject to that of the 21-year-old (completing) the obligatory medical test and agreeing with Chelsea FC on the terms of the player's contract."
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