Winger Anya spent last season on loan with the Hornets from sister club Granada and has now agreed a three-year contract.
The 25-year-old former Wycombe youngster made 29 appearances last season as Gianfranco Zola's side reached the play-off final.
Vicarage Road chief Zola has also swooped for free agent Brown, who was released by Manchester United in May.
The 21-year-old defender, the younger brother of former United star Wes Brown, has put pen to paper on a two-year contract.
The Hornets have also confirmed that full clearance has been granted by the Football League and the FA regarding the eight players they signed last week.
Former loanees Almen Abdi, Marco Cassetti, Cristian Battocchio and Daniel Pudil agreed permanent deals along with Gabriele Angella, Marco Davide Faraoni, Diego Fabbrini and Javier Acuna, who all arrived from Watford's other sister club Udinese.
The captures of Anya and Brown take Zola's total summer signings to 13.