And compatriot Luis is thrilled to have him back, having won La Liga with him during his first spell in the capital before joining him at Stamford Bridge during the 2014-15 season.
The 30-year-old provided another timely reminder of his huge ability during the worldwide break, netting a hat-trick as Argentina crucially beat Ecuador 3-1 to avoid an embarrassing failure to qualify for the World Cup.
'I have seen [Juan Carlos] Valeron do things nobody could do.
Filipe Luis is used to coming into contact with the world's best players and is a team-mate of Neymar at global level with Brazil. "Nobody does that as well as Diego Costa".
Luis also had positive words to say about Costa's soon-to-be striking partner Antoine Griezmann, backing the Manchester United target to stay at the club for "much longer".
It appeared at one stage over the summer that the France worldwide could be moving on, but interest from the likes of Manchester United eventually came to nothing and the 26-year-old committed to a new five-year contract.
"Messi is so good that he could win the league with only a mediocre team, which is not the case [with Barca]", he told El Mundo. Then they get more attention.
"In the end, no matter how he spoke with other clubs, he always wanted to stay and here he is, happy and at ease".
"Often players talk when they feel they are not being valued as they deserve".
"He would have had many offers from many teams".
'And that is fair as Griezmann is doing great here. We hope the fans understand this and everything gets back to normal, although he has been scoring goals, and goals cure everything.
Messi has 11 goals in seven league outings so far this season.