Varela had a successful trial with United last season and Moyes has agreed to complete a deal to sign the full-back from Atletico Penarol for an undisclosed fee, even though the 20-year-old had played just one game for his club.
Moyes, who replaced the retired Alex Ferguson at Old Trafford at the end of the season, will be able to see Varela in action immediately as he is in Uruguay's squad for the Under-20 World Championships in Turkey.
Varela will provide competition for the likes of Rafael and Fabio da Silva, Patrice Evra and Alexander Buttner.
"Manchester United is pleased to announce it has reached agreement to sign 20-year-old defender Guillermo Varela from Uruguayan club Atletico Peñarol for an undisclosed fee," a statement on United's website confirmed.
Moyes seals first deal as Man United land Guillermo Varela
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