Jessica Alba is now formely taken!

Jessica Alba and Cash Warren have gotten married, PEOPLE confirms. The couple quietly wed Monday, says her rep, Brad Cafarelli.

"According to a source, they were married in the Beverly Hills courthouse's ceremony room under an arch of green silk foliage and white flowers. They were casually dressed, with Alba wearing a long blue dress and her hair back in a ponytail.

"She looked happy but nervous," the source says.

Warren, in a white shirt and brown pants, arrived with Alba at about 11:30 a.m. on Monday, applied for a marriage license and waited about 40 minutes for the paperwork to be processed before a staff member from the courthouse married them, the source says.

Nobody else attended the wedding, the source adds. "

Good-luck to the happy couple!