Cleverley was placed in charge at Vicarage Road on a temporary basis when Valerien Ismael was sacked in March.
He 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.
