The Dutch defender was at the Bridge yesterday to see his new side beat Manchester City 3-0.
He has passed his medical and has signed for about £6m from Hammburg.
He is 24 and has 15 caps for Holland.
"In a short squad and in a country where you can have only 16 players for a match, it's important to have cover for many positions," said Chelsea boss Jose Mourinho.
"So now I can have Boulahrouz, Ricardo Carvalho and John Terry - three options for the centre. I can have Paulo Ferreira and Boulahrouz - two options for the right side; I can have Boulahrouz and Wayne Bridge - two options for the left side."
"He is a good competitive player and will be a good addition to our squad," Chelsea's assistant manager Steve Clarke told Chelsea TV.
"It is important to have one or two players around the squad who can play in a number of different positions."
Boulahrouz is available for Chelsea's European campaign and is in the squad for Wednesday's Premiership game at Middlesbrough.