Arsene Wenger closes in on Euro 2012 star, Bologna want to keep hold of Ramirez and Diamante, while Andriy Shevchenko will decide his future soon.
Transfer talk: June 26 - Arsenal complete Giroud deal
Giroud, who was part of the French Euro 2012 squad which was knocked out by Spain in the quarter-finals on Saturday, scored 25 goals to help Montpellier win their first Ligue 1 title last season, and will now aim to make an impact in the English Premier League.
The forward has joined on a 'long-term contract' for an undisclosed fee, thought to be in the region of £13million (Dh 74m).
Giroud, whose contract with Arsenal will officially commence on July 1, said on the club's official website: "I am delighted to be here at Arsenal and to be part of one of the great teams in English football. It's a huge satisfaction to join this great club and it's been a dream since I was young to play in the Premier League."
He added: "I was attracted by the philosophy of football and Arsene Wenger's 'touch' at this club."I have always admired Arsenal with its great history and reputation, and I now hope to achieve great things here. I'm very proud to be a Gunner and I will give my best for all the Arsenal fans."
Wenger, who is at the European Championship working as a media pundit, is convinced Giroud can be a big hit at Arsenal.
Arsenal could also now resurrect interest in Yann M'Vila after Champions League finalists Bayern Munich cooled their interest in the Rennes midfielder.
Bologna insist they have no intention of selling Euro 2012 penalty hero Alessandro Diamanti this summer.
Diamanti, who scored the winning spotkick for Italy in Sunday night's shoot-out win over England, is a reported target of several top clubs in Europe.
The 29-year-old attacking midfielder was co-owned by Brescia and Bologna before the latter bought the player outright last weekend.
"Diamanti is a player that gives everything and it is likely that he will remain with us next season," club president Albano Guaraldi said.
The former West Ham player is under contract with Bologna until June 2016.
Guaraldi also revealed that coveted playmaker Gaston Ramirez could also remain at the club.
The Uruguay international joined Bologna from Penarol in 2010 and is a reported target of Manchester City, Liverpool, Inter Milan and Juventus this summer.
"I don't exclude that Ramirez could stay," Guaraldi said.
"We have had offers for him but he is worth at least 20million euros.
"If the right offer comes along then he could leave."
Ukraine striker Andriy Shevchenko admits he may yet quit playing football altogether after his side's exit from Euro 2012.
The 35-year-old forward's deal with Dynamo Kiev expires in July, although the club has offered Shevchenko a new contract.
But the former Chelsea man says he may hang up his boots for good.
"At the moment, I have not made a decision about my future - whether to continue playing football or retire, whether to stay in Ukraine or leave the country," he admitted during a visit to his old school in Kiev.
"I have offers from clubs abroad and from Dynamo Kiev. Let me take a breather after the Euros and make a decision. I will certainly stay in football ... Football is a bit more than a game for me. It is what I live for."
New Norwich City manager Chris Hughton is to step up his bid to retain club captain Grant Holt after securing goalkeeper John Ruddy on a new four-year deal.
The 25-year-old stopper's form was enough to earn him a call-up into the England squad for Euro 2012, only for him to suffer a broken finger and be forced out of contention.
And with deals already in place for defender Russell Martin and Andrew Surman, Hughton now wants to keep the 31-year-old forward, who scored 15 goals last season for the Carrow Road side.
Holt had a transfer request rejected at the end of last season, with West Ham having reportedly bid £4m for the forward.