Bassett made history earlier this month when she became the first woman to lead a Birmingham City side out at the club's 107-year-old St Andrew's stadium in their Champions League last 16 tie against FK Zorkiy Krasnogorsk.
That proved to be the 30-year-old's last match for the club she has spent 11 years with during two spells after Birmingham announced she had opted not to renew her contract.
Bassett will now join up with Chelsea ahead of the club's participation in next week's International Women's Club Championship in Japan and she revealed she cannot wait to get going for her new side.
"The move is absolutely brilliant and I can't wait to get started," Bassett said. "It's great that we've got an opportunity like Japan to get straight in to the action rather than have to wait until pre-season.
"Chelsea is a massive club with a big-club mentality so it is a new challenge for me, which is exciting. The staff and the players are really ambitious here so for me to be part of that is something I am over the moon with.
"This is an exciting chapter in my career and I want to see if I can be part of something successful again with a new club. I want to be part of getting this club where it wants to be."
Chelsea Ladies manager Emma Hayes added: "We're fortunate enough to have signed a wonderful leader in Laura.
"Her wealth of experience will bring Chelsea's performances to another level. We are always interested in good people as well as good players at this football club and Laura certainly fits that profile.
"Bass is a quality defender and we're all looking forward to working with her. The tournament in Japan will be a great way to integrate her in to the group."