The 21-year-old will star alongside new Time Lord Matt Smith in the new series, to be broadcast next year.
Gillan has already appeared in the drama, having played a Soothsayer in The Fires Of Pompeii in the last run.
"I am absolutely over the moon at being chosen to play the Doctor's new companion. - I just can't wait to get started," she said.
'Incredible actor'
"The show is such a massive phenomenon that I can't quite believe I am going to be a part of it.
"Matt Smith is an incredible actor and it is going to be so much fun to act alongside him," she added.
Head of Drama, BBC Wales, Piers Wenger said she brings "energy and excitement" to the role.
"When she auditioned alongside Matt we knew we had something special," he said.
Writer and executive producer Steven Moffat said they saw some "amazing actresses" but Gillan "walked through the door the game was up".
He described her as "funny, and clever, and gorgeous, and sexy. Or Scottish, which is the quick way of saying it".
"A generation of little girls will want to be her. And a generation of little boys will want them to be her too," he added.
Gillan, from Inverness, developed a love for acting after attending several youth theatre groups and taking part in various school productions.
At the age of 16, she decided to pursue her career further and left school to study acting at Edinburgh's Telford College.
She went on to secure a place at the Italia Conti drama school in London and landed her first role in the Scottish drama Rebus.
Parts in Channel 4's Stacked, The Kevin Bishop Show and James Nesbitt's forthcoming film Outcast followed, but the role in Doctor Who is her first high profile to date.
Also in the Fires of Pompeii she was one of the soothsayers.....just like Freema Agyeman has a role in series 2 before become the Doctors full time assistant in seeason 3.
