The Frenchman will sign a two-year contract at San Siro, with the Blues set to receive €6.5 million ($7m, £6m).
Giroud has been restricted to just five Premier League appearances for Chelsea in 2019-20.
The France international remains determined to get his hands on the Premier League title having crossed London without a winners' medal to his name
Olivier Giroud admits to having left Arsenal with “unfinished business” and is determined to right his Premier League wrongs with Chelsea.
The France international brought a five-and-a-half-year stint with the Gunners to a close during the January transfer window.
A deadline day switch saw him cross London, with Chelsea acquiring a proven performer who had plundered more than 100 goals for their local rivals.
Giroud was, however, to leave Emirates Stadium with just three FA Cup winners’ medals to show for his efforts and he is eager to land English football’s biggest prize after trading red for blue.
"I don't know if we can really call it a regret but I have a little feeling of unfinished business because I would really have liked to have won the Premier League with Arsenal," the 31-year-old told SFR Sport.
"You don't just wipe away five-and-a-half years like that. I have said it often enough - it was my ultimate goal.
"Having said that, it's not over, I'm still in the Premier League, now I'm at Chelsea. For this year, I think it's over for the title, but next year, we'll come to it with great ambitions.
"I still want to win it before I end my career."
Giroud penned an 18-month contract with Chelsea after completing an £18 million move.
He has already opened his account for new employers, in an FA Cup clash with Hull City, but still has plenty to prove if he is to see regular game time and chase down his ultimate goals.
A 2-1 defeat to Manchester United in their latest outing has dropped the Blues out of the Premier League’s top four, while a 1-1 draw with Barcelona in the first leg of their Champions League last-16 encounter means Antonio Conte’s side face the unenviable challenge of having to score at Camp Nou in the return date on March 14.
SOURCE: ALL FOOTBALL
Olivier Giroud's agent has arrived in London to finalise the striker's move to Chelsea.
Arsenal have agreed to sell the France international for just under £18million and the player's representative is in town to ensure the deal goes through.
The Gunners have agreed to sell the France striker to their London rivals in a move that allows Pierre-Emerick Aubameyang to move to the Emirates in a club record £55.5million deal — and sees Michy Batshuayi sign on loan for Borussia Dortmund.
Giroud came on for the final 15 minutes of Arsenal's surprise 3-1 defeat by Swansea on Tuesday night as the clubs ironed out the final details, with the fee expected to be £18m plus add-ons.
In the wake of his side's disappointing display in South Wales, Wenger paid tribute to his departing forward.
It's a tribute to Olivier (that he played) because he is a guy who gave great service to the club, he never let us down on the commitment front and saved us many times,' Wenger said.
'I have absolutely no doubt, when I ask him if he is ready to commit and he says yes. I have no problem with that and put him on because it was needed. Unfortunately he couldn't help us.
'I took him from Montpellier and made him a strong international player for France. We have come together through good and bad but always his behaviour was top, top class.'
Giroud's transfer had earlier reached an impasse as talks between Arsenal and Chelsea broke down over the fee. However, Wenger's willingness to help Giroud achieve his move is understood to have been a key factor.
SOURCE: All Football
Arsenal striker Olivier Giroud could be on his way to join Everton in January in order to increase his chances of making the France squad for the 2018 World Cup in Russia.
Giroud was said to be close to securing a move to the Toffees in the off-season as a direct replacement for Romelu Lukaku but rejected the transfer at the last minute.
Ronald Koeman suggested that the club's poor form at the start of the season that culminated to his eventual dismissal was down to the failed deal for the towering striker.
However, with Giroud only starting one Premier League game for the Gunners this season, the former Montpellier forward seems open for the second round of negotiations with the Merseyside club.
"I have the World Cup at the back of my mind weekly, almost daily." he told reporters last month "Each time I go onto the pitch, it’s to be more clinical and keep on track for the World Cup."
Wayne Rooney, who has been in scintillating form with 10 league goals so far this season has spoken of his admiration of the 31-year-old when asked about his possible arrival.
"I think we could do with another striker in," Rooney told TalkSport. "The one player for me who has to start is Olivier Giroud. He scores goals and every time he comes on he scores, he's a handful and hard to play against.
"For me, if he starts games for Arsenal they are a better team."
