Cameroon international Song, 24, passed his medical at the Nou Camp in a £15million deal and was confirmed as a Barcelona player, signing a five-year contract with the Catalan giants.
Sahin representatives have been in Madrid looking to arrange the 23-year-old's departure after it became clear he was no longer in Jose Mourinho's first-team plans.
Liverpool have also expressed an interest in the Turkey international, but Arsenal are reported to be his preferred destination, although that will be on a season-long loan rather than a permanent move, which is expected to be ratified within the next 24 hours.
The departure of Song comes just a few days after former captain Robin van Persie was sold to Manchester United, the Holland international having announced he would not be signing a new deal.
However, the midfielder still had three years left on his Arsenal contract, and Gunners boss Arsene Wenger intimated after Saturday's goalless draw with Sunderland at Emirates Stadium there was perhaps more to the transfer, with reports the player had become a disruptive influence.
Wenger also made it clear he would still be open to more new arrivals, having already brought in Olivier Giroud, Lukas Podolski and Spain international Santi Cazorla, who impressed in midfield on his debut.
"We are looking to bring one more midfielder in of course, and maybe one defender as well because we still feel we are short in some positions," Wenger told Arsenal Player.
Watch: Song completes Barcelona move... More Videos
Long-time target Yann M'Vila is still on the radar. However, Rennes have named Tottenham as one of the firm interested parties, with Zenit St Petersburg and another anonymous club also at the table.
The arrival of Cameroon defensive midfielder Jean Makoun on loan from Aston Villa could further hasten M'Vila's departure, although Rennes general manager Pierre Drerossi has not yet ruled out the player staying for another season if their £17m price tag is not met.
While Wenger could have reinforcements in place for Sunday's trip to Stoke, it is clear the manager expects a much-improved attacking display after drawing a blank despite dominating Sunderland for long spells.
He said: "We didn't lose, but it is frustrating when you are home with everyone here and you do not create more chances than we did.
"It is very difficult to understand."
Cazorla certainly was the stand-out pick of Wenger's summer additions, with Podolski struggling for openings while Giroud missed the best chance of the game with nine minutes left when he blasted wide from 12 yards.
Podolski bagged 20 goals for club and country last season, and German centre-half Per Mertesacker feels the Gunners will soon see the best of the former Cologne marksman.
"It was tough for him [on Saturday] because it was his first game up front," said Mertesacker, back from an ankle injury which ruled him out of the end of last season.
"He will get used to the game, switch on quickly and score a lot for us.
"You have seen that he has a good technique and he is good in possession.
"We have the players who can pass him the ball. He is a good finisher too and we will see that in a couple of weeks."
Wenger felt Arsenal lacked a cohesive balance in attack.
Mertesacker agreed. He told Arsenal Player: "We saw a lot of misunderstandings [against Sunderland], especially in the first half. One guy maybe wanted the one-two, the other in behind.
"So we need a bit of time, especially with the new players, but I think it is coming."
Marouane Chamakh, meanwhile, has been linked with a loan move to Tottenham. However, sources at Arsenal's north-London rivals maintain there is no interest in the Morocco frontman.