"It's something I hadn't thought of before, but now I know I feel good about it," the music mogul said at the One Direction film premiere on Tuesday night.
It is the first time that the X Factor judge has confirmed that he and the New York socialite are expecting a child.
"Things are changing in my life right now, for the better," the 53-year-old told the BBC.
"She [Lauren]'s a very special girl."
Lauren reached a divorce settlement with her husband of ten years last week.
Her property mogul husband filed for divorce last month, shortly after the news broke of his wife's infidelity with his close friend .
They have also come to an agreement to share joint custody of their seven-year-old son.
Simon - whose fortune is estimated at $368million - was cited as a "co-respondent" in the court papers for adultery.
According to TMZ, Lauren will live in New York so that she can be close to her son. The 36-year-old US socialite is believed to be 10 weeks pregnant with Simon's baby.
The deal was agreed in Manhattan on Wednesday, with Lauren said to have won half of her $4million pre-nuptial agreement.
Simon spoke to press ahead on the red carpet ahead of the London premiere of 1D's documentary movie This Is Us.
The TV personality, who signed the band to his record label after they became X Factor finalists in 2010, co-produced the film. "It has been my dream come true to produce a film," he said. "But without their fans, this couldn't have happened."
"I feel like a proud father."