Cleverley was placed in charge at Vicarage Road on a temporary basis when Valerien Ismael was sacked in March.
The 34-year-old has managed one win, one loss and five draws during his seven matches with the Hornets.
Watford are currently 15th in the second-tier table with two games left against Sunderland and Middlesbrough.
They had lost six of their last eight league games before Ismael was axed in the midst of a disappointing season for a team expected to push for a play-off place.
Former England international Cleverley joined Watford on loan from United in 2009-10.
He returned to Watford from Everton in 2017 before retiring last year after an injury-plagued spell in the latter part of his career.
Cleverley made his first move into coaching with Watford's youth academy before taking on the interim head coach role last month.
