The contract was given to Hope North East by national charity Crisis for their new Hope 4 A Home project.
The charity said the money will help single non-priority homeless people find new homes and independence.
A Middlesbrough Council spokesperson said such homeless people placed "a high demand" on social housing teams, and the money will help the situation.
Crisis has allocated £3m in total, provided by the Department of Communities and Local Government.
The project is one of over 70 new local projects across England, adding to an existing 49 that have already helped more than 1,000 homeless people into a home.
The project would help the homeless build a better future for themselves.
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