The 20 year old - a member of the Scottish Rugby Scademy - made his Warriors debut against the Ospreys during the 2016/17 season and has since gone on to make five appearances for the club.
Nicol played for Stirling County in the BT Premiership last season and played in the club's first ever BT Cup Final appearance on Silver Saturday.
Having represented Scotland throughout the age-grade system, Nicol was a member of the Scotland U20 squad that finished fifth at the 2017 U20 World Championships in Georgia. Also in that squad were Bruce Flockhart and Robbie Nairn, both of whom have also signed professional contracts ahead of the 2018/19 season.
Speaking about his first professional contract, Nicol said: "I've loved every minute of my involvement so far. I've played more than I thought I would have, but I now know what is expected from me and the game time has put me in good stead for life as a professional.
"I've learnt loads from the senior players and coaches already. Dave (Rennie) likes to play a fast-flowing game, so I've had to work on things, but I've enjoyed adding another aspect to my game and I'm looking forward to next season as a professional player."
Glasgow Warriors Assistant Coach Kenny Murray said: "It's great for us that, once again, the Academy system has produced another promising player," said Murray.
"Adam has shown, both at U20 level and when he's been in and around our squad, that he has great potential to play at the top level as a prop.
"There are areas of his game that he needs to develop, and we're looking forward to getting him into our environment to help him improve."