Her predecessor, Meredith Vieira, had an on-air going-away party Wednesday.
Curry had been on the show since 1997 as the regular newsreader and has filled in dozens of times as co-host.
She referred to that in her opening, saying, "I'm Ann Curry, in for I guess nobody this morning - me, myself and I. It's nice to be able to say that, isn't it?"
Lauer welcomed her, saying she had already been on the show so long that "it's a little bit like a member of the family moving to a new seat at the table."
The Associated Press contributed to this report.