The La Liga champions had a clause included in the Turkish international’s contract permitting the new board to sell him back to Atleti for 10 percent of the initial transfer fee.
Bartomeu was re-elected president following the elections on the 19th. The Champions League title holders had until the 20th to send Turan back to his former club.
Turan will remain at Barcelona on a five-year contract after completing his £24 million move last month.
The 28-year-old winger will not however, be able to register as a Barcelona player until January due to the La Liga winners serving a FIFA transfer ban.
Barcelona can make transfers but new players are unable to play until the new year.
Turan was expected to get loaned out for six-months but Barcelona manager Luis Enrique has insisted that he remains at the club.