The former club captain has been in charge on an interim basis for the last seven games.
The 34-year-old took over as the interim boss following the departure of Valerien Ismael at the start of March.
In that time Watford have only lost once, and that was a highly controversial 3-2 defeat at Southampton. Cleverley made more than 180 playing appearances during two spells at Vicarage Road, the first on loan from Manchester United as a 19-year-old when he spent the entire season with Watford and ended up being voted Player of the Season.
Cleverley went on to become club captain but his playing career came to an end last season due to injury.
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