Brown has faced repeated rumours of a threat to his leadership since taking over from Tony Blair in 2007 but has held on to his role.
His opponents within Labour say what they call his lacklustre leadership will ensure electoral defeat.
Hewitt, a former health secretary, and Hoon, a former defence minister, who was also Labour's chief whip, said: "This is a clear opportunity to finally lay this matter to rest.
"The continued speculation and uncertainty is allowing our opponents to portray us as dispirited and disunited.
"It is damaging our ability to set out our strong case to the electorate. It is giving our political opponents an easy target."
Hoon and Hewitt are seen as allies of Blair and it is thought unlikely that they will receive enough support to topple Brown.
But the timing of Wednesday's letter is awkward, with British political parties effectively having started election campaigning this week after the Christmas break.
Brown is expected to call the election for May.