Ryan Christie agreed a "dream" four-year contract with Celtic and immediately returned to Inverness Caledonian Thistle on a season's loan.
The 20-year-old was given permission to discuss personal terms with Celtic after they made a further approach after an initial £500,000 offer.
Celtic have the option to recall the midfielder in January.
"I'm buzzing to be honest," he said. "I've been a supporter all my life, something I got from my dad."
Father Charlie, a former Inverness midfielder and manager, also had a spell at Celtic Park.
"It has been a pretty crazy 24 hours to get it all done and dusted, but to finally put pen to paper is an incredible feeling," his son told Celtic's website.
"I was first told at the weekend that there was interest. You never know how much to believe in that, but as soon as I was told I had permission to speak to the club I was over the moon and just desperate to get it finished.
"It might sound a bit sad saying it's a dream come true, but it really is and it will be brilliant to play at a place like Celtic Park."
"It's a chance for me. It's going to be tough, it's going to be a challenge, but it's one I want."
Christie came through the youth ranks at Caledonian Stadium, became a first-team regular last season and is pleased to return there on loan.
"It gives me that wee bit of time to get settled and get ready so that when I come back to Celtic I hit the ground running," said the Scotland Under-21 international.
"I know it's going to be a step up, but I have to challenge myself and I wouldn't have signed if I didn't think I was up for that challenge.
"There are a lot of targets we're trying to hit at Inverness so that's my short-term plan.
"John Hughes has been superb. I don't know if him being an ex-Celtic player has helped, but he had a word in my ear before Saturday's game just to put it at the back of my head, but he's had nothing but support for me since it broke."