Lianne Sanderson (20) and Anita Asant(23) are both senior England internationals and first-team regulars for the Gunners girls, who completed a third successive Premier League and FA Cup 'Double' last season.
Islington-born Akers has managed the Ladies for 21 years, in which time they have won 29 major trophies, and he expressed his disappointment with their decision.
"The first I heard about it was when I got a text from Lianne," he admitted. "You think you've got the respect of players, and then they do that. It's a sorry state of affairs.
"I am disappointed to lose them but they have made their mind up to go and I would never keep anybody around the club who is not happy. We have got to accept it."
Sanderson, top Premier League scorer for the last two seasons, said: "I've been at Arsenal for 11 years so it's not been an easy thing to do to leave them.
"But Chelsea are an up and coming team and hopefully I can make a positive impact.
"I had various conversations with Vic last season about how I felt. He obviously didn't realise I was as keen as I was about leaving, so when I told him it came as a bit of a shock."