Chelsea said in a statement that a club record fee -- put at 38 million euros (25.8 million pounds) by Essien's former club Olympique Lyon -- had been agreed.
"He is a Chelsea player," a Chelsea spokesman said.
Essien has secured a work permit and the club is awaiting international clearance for the 22-year-old to play, potentially on Sunday at home to Arsenal.
The protracted transfer was marked by the reluctance of Lyon president Jean-Michel Aulas to lose the player but Essien's stated desire to join Chelsea.
Voted the Ligue 1's Player of the Year last season, Essien is expected to compete with Claude Makelele for a place alongside Frank Lampard in central midfield.
Along with retaining their Premier League title, Chelsea coach Jose Mourinho is aiming to add the Champions League this season after losing in the semi-finals to eventual winners Liverpool last term.
Chelsea are expected to unveil the player at a news conference at their Cobham training ground at 1245 BST.
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