The 19 year-old is moving to Villa Park for a fee rising to £10.5m.
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Alysson will undergo a Villa medical before the January market opens ahead of completing his transfer.
The deal initially worth £8.7m plus a further £1.8m in performance-related add-ons. Gremio will also retain a 10 per cent sell-on clause.
Alysson has a deal to 2029 with Gremio and has made 43 appearances for the first team.