The 20-year-old is understood to have been signed for a fee in the region of £7 million (€8m) after impressing during Uruguay’s victorious Copa America campaign, winning the award for the best young player at the tournament in the process.
The centre-back had attracted reported interest from Tottenham and was understood to have been offered to Arsenal, however it is Liverpool who jumped to the front of the queue and snapped up the highly-rated youngster.
It was clear the Anfield club were in the market for a centre-back following the extensive links with Phil Jones before he signed for Manchester United and the need for more numbers in that area was solidified when Sotirios Kyrgiakos left for German side Wolfsburg.
Coates, who has been capped five times for Uruguay's senior side, has joined Liverpool on a long-term contract and the club was able to confirm the signing after the Nacional youth-product passed a medical as well as being granted a work permit.
Before he makes his debut for his new club, Coates is due to travel to Kiev where Uruguay are set to face the Ukraine in an international friendly on Friday.