Chelsea have signed Arsenal striker Olivier Giroud on an 18-month deal for about £18m.

France international Giroud, 31, leaves Arsenal having scored 105 goals in 253 games since signing from Montpellier for a reported £12m in June 2012.

Borussia Dortmund have also confirmed a deal to sign Chelsea forward Michy Batshuayi until the end of the season.

Earlier on the closing day of the winter transfer window, Dortmund sold Pierre-Emerick Aubameyang to Arsenal.

"Chelsea is one of the biggest teams in the Premier League - they have won maybe the most trophies in the last six or seven years," said Giroud in a statement.

"It's a massive club and I am proud to sign for Chelsea, and I'm looking forward to playing."

Giroud's final appearance for Arsenal was as a substitute in Tuesday's 3-1 defeat by Swansea.

"Oli is a guy who gave great service to the club. He never let us down on the commitment front and he saved us many times," said Arsenal manager Arsene Wenger.

"We signed him from Montpellier and he became a strong, regular international player for France, and we have gone together through good and bad. But always I believe that his behaviour has been top, top class.

"He always had his heart 100% in the team and he was committed."