The young defender has received a work permit and will join Kenny Dalglish's squad immediately, with compatriot Suarez already welcoming him to Anfield
The Reds agreed to raise their transfer offer to meet the club's valuation of the starlet. Liverpool will pay the Uruguayans £4.9 million for their star, in a transfer that, as requested by Nacional, does not involve any third-parties or intermediaries.
The completion of negotiations was confirmed by Nacional vice-president Olmos, who also assured that the youngster had received permission to work from the UK authorities.
"There were moments of tension [during talks], but as civilised people we finished them well," the official told Nuevo Tiempo, before laying any worries over the work permit to rest.
"[Liverpool] took care of it today. They went to London and completed the necessary paperwork so that he can play."
Coates is expected to be officially announced as a Liverpool player on Wednesday, with the transfer window closing at 11pm UK time.