The 25-year-old actress was unveiled to the public on Wednesday (March 21) and will join the sci-fi drama at Christmas.
Tennant told Digital Spy. "She'll have a brilliant time. I'm very jealous of [someone] starting out on that extraordinary journey."
> Jenna-Louise Coleman: Ten Things about the new Doctor Who star
However, the Scottish actor - who played the Tenth Doctor from 2005 to 2010 - warned Coleman to "keep [her] nose clean" and "watch [her] back".
"You're suddenly rocketed into a world of attention," he explained. "You just need to watch your back a little bit, but it's wonderful and it's such an exciting thing to be starting out on."
Current Doctor Who lead Matt Smith recently revealed that he is "very excited" to work with Coleman.
"I was part of the audition process where we met a number of wonderful actresses," he said. "But I think Jenna responded to Steven [Moffat]'s writing in the most interesting way."
Tennant's new film The Pirates! In an Adventure with Scientists is released on March 28 in the UK and April 27 in the US.