The English champions will pay Arsenal five million pounds ($9.5 million) for the exchange.

"Chelsea FC and Arsenal have agreed terms for the transfers of Ashley Cole and William Gallas," both clubs said in a joint statement on Thursday.

"Both players have agreed personal terms and passed their respective medicals."

The move, which was completed just before the close of the transfer window, put an end to the protracted summer saga.

England international Cole's relationship with Arsenal strained since he was involved in a tapping-up row with Chelsea last season.

Arsenal were reluctant to sell the 25-year-old for cheap but the inclusion of Gallas in the deal paved a way for leniency in the Gunners' demands.

Gallas was unhappy with the role he plays for Chelsea due to his versatility as he prefers to play in the heart of defence.