Jones told Scyfilove that Eccleston, who played the Ninth Doctor in 2005, had enjoyed Smith's theatre performances in the past.
"[Matt] came over to me when I was applying the make-up and said it looked fantastic, and we got chatting," he explained. "I was able to tell him that I had been talking to Chris Eccleston recently, who said he'd seen Matt in a couple of plays and thought he was a great choice for Doctor Who."
Jones claimed that Smith was pleased to have received his predecessor's approval.
"[Matt] was quite blown over to hear that Chris thought he was good," he said.
Jones originally worked alongside Eccleston in 2005 and returned to Doctor Who last year for the two-part story 'The Hungry Earth/Cold Blood'.
The show will return to BBC One this Christmas for a one-off special.