It's not the first time Smith has met Tennant. They both attended Steven Moffat's birthday party.
The 29-year-old actor also gets excited to meet the other Doctors, and often forgets that he plays the time traveller himself.
Matt told 'BBC Breakfast': "I saw David on Saturday it was Steven Moffat's birthday party. I was like, 'It's Doctor Who!' I saw Peter Davison as well who was at the same party. Steven was very excited that there was more than one Doctor there. And I can't help but go, 'Oh my God. It's Doctor Who!' But then I realise I'm the Doctor."