The 53-year-old rocker-turned-photographer and Alicia - who already have 21-month-old daughter Mirabella Bunny Grimaldi-Adams together- welcomed Lula RosyLea into the world earlier this week. Brian`s representative said: "BryanAdams and AliciaGrimaldi welcomed their second babygirl in London earlier this week."
Explaining the unusual moniker, Bryan told People: "Lula RosyLea decided to arrive at tea time. RosyLea is cockney rhyming slang in London for `cup of tea` and the name Lula comes from Gene Vincent`s song `Be-Bop-A-Lula.`"
Brian joked about the arrival of his "Easter bunny" Mirabella last year.
Announcing the birth of his daughter, he said: "I`m really proud to announce on 22 April, Mirabella Bunny was born. Mother and baby are both well and happy. Thanks in advance for your kind thoughts and wishes.
"She arrived like all good Easter bunnies on Easter Friday."
Friends of Alicia - who is believed to be living with the singer-and-photographer in London - were said to be shocked when Bryan announced the pregnancy last March as many people had no idea they were even dating.
One insider said: "Many of their friends still don`t even know that they are a couple, but they are living together at his house."
Alicia is a charity activist and one of the trustees of the BryanAdams Foundation, a charity registered in the UK.