PIC: Alanis Morissette's Baby Bump!

Credit: Anthony/PacificCoastNews.com

Alanis Morissette announces exclusively in the new Us Weekly that she is expecting her first child -- and, on Wednesday, she showed off her bump for the first time.

Stepping out for coffee in L.A. with rapper-husband Souleye, she was all smiles.

Later that evening, she told E!'s Chelsea Handler her pregnancy came as a pleasant surprise. "I actually thought I wasn't," said the singer, 36. "I had just sort of said in passing [to my doctor] that I was a little late ... And he said, 'Let's take a quick look.'"

The doctor told her a short time later it appeared she was pregnant.

"And I said, 'There's still a chance that I'm not, though, yes?' And he said, 'About as likely as my getting a sex change,'" she recalled. "And I said, 'So, when are you getting your sex change?'"

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On her Twitter page, she gushed, "Yes, happy news....i'm pregnant :) we're so excited to start our family.... xo a"