Atletico Madrid have signed midfielder Geoffrey Kondogbia from Valencia, the two clubs announced on Tuesday.
Kondogbia, who has played internationally for France and the Central African Republic, has signed a contract until 2024, Atletico said in a statement.
La Liga rules allowed Atletico to buy outside the transfer window after Arsenal activated Thomas Partey's 50 million euro ($58 million) release clause on the last day of the summer transfer window.
Kondogbia will cost Atletico around 10 million euros, according to reports in the Spanish press, with a further 2 million euros due in variables. Valencia will also take 10 per cent of any future sale.
"A talented and strong midfielder joins Atletico Madrid," the club said. "His physical presence, defensive solidity and striking ability from distance make him an all-round player in central midfield."
Thomas had been one of Atletico's most important players but the club have attempted to fill the void with the signing of Kondogbia, as well as Arsenal's Lucas Torreira who joined on loan.
Valencia, though, will not be able to replace Kondogbia and letting the 27-year-old go continues the club's drastic selling policy, which has been hugely unpopular with the fans.
In a statement issued in August, Valencia owner Peter Lim said: "We need to reduce the cost of our team. First, for the obvious reason that we are not in the Champions League. We only have La Liga in which to compete, and we will need fewer players."
"A bankrupt club is not a better club," he added.
Valencia's new coach Javi Gracia has already complained publicly about the club failing to replace players sold and the team have endured a poor start to the season in La Liga, sitting 13th, three points above the relegation places.
A brief statement, titled 'So Long, Geoffrey Kondogbia' on social media, read: "Valencia CF have formalised an agreement with Atletico Madrid for the permanent transfer of Geoffrey Kondogbia."