AC Milan have completed the signing of Arsenal midfielder Mathieu Flamini on a four-year contract - but the club expect to miss out on Chelsea's Didier Drogba.Flamini is out of contract with the Gunners at the end of the season and today agreed to join the Italian club in a deal which will begin on July 1. Milan have also been strongly linked with Chelsea striker Drogba in Europe but Milan sporting director Ariedo Braida does not anticipate the Ivory Coast forward joining Flamini at the San Siro this summer. He told PA Sport: 'Drogba is a very interesting player that many clubs would want to have but he is under contract at Chelsea and I believe he will remain at Chelsea next season.' As for France international Flamini, Braida revealed Milan coach Carlo Ancelotti is a great admirer of the 24-year-old. 'I have to say Flamini was a player that Ancelotti really wanted and Milan is like a family, where decisions are made jointly,' he said. Arsenal had hoped Flamini would agree a deal to stay at the Emirates Stadium, but they always knew it would be difficult with outfits like Juventus and Milan coveting the player. 'Flamini is not an unknown player,' said Braida. 'Just like Didier Drogba isn't. 'I'm not surprised by his talent and I assume several teams would have wanted his services. 'Although no negotiations are ever easy, it wasn't difficult to convince Flamini to join Milan. 'Flamini has made a choice as his contract with Arsenal is coming to an end and we are delighted he has chosen Milan. 'He is a very good player and he can offer a lot to the team.' Flamini expressed his joy at the move after finalising terms with the Serie A outfit. 'I am extremely happy. Thanks a million,' he said. Despite the offer of a lucrative new five-year deal - understood to be worth around £55,000-a-week - from the north London club, Flamini's head was turned by Milan's interest. Juventus were also reported to be tracking the player, who has formed a fine partnership with Cesc Fabregas this season after looking to be on his way out of the club at the end of the last campaign. He put in an impressive performance at the San Siro as Arsene Wenger's team knocked Milan out of the Champions League at the last-16 stage in March. It is understood the former Marseille man said his goodbyes to some staff as he left the car park after yesterday's home win over Everton in the Premier League. He will compete for a place in the Rossoneri midfield with Brazil star Kaka and the Italy trio of Gennaro Gattuso, Andrea Pirlo and Massimo Ambrosini. Milan beat city rivals Inter Milan 2-1 today to climb into the final qualifying place for the Champions League, leapfrogging Fiorentina who lost 2-1 at Cagliari. Flamini's last match as an Arsenal player will be Sunday's Premier League trip to Sunderland.