Andy Burnham is set to spend more than £700,000 to help migrants claim benefits, get housing, and access public services.
The Greater Manchester Combined Authority, run by the mayor, will spend the money on schemes to help refugees overcome "barriers to accessing housing, welfare and local services".
These schemes largely target refugees who have already been granted asylum.
Refugees are offered "new community guidance" and additional support through a lodging scheme as part of the "Safe Transitions" programme.
Greater Manchester currently hosts more than 8,500 people in asylum support accommodation, including hotels and lodgings throughout the city.
Mr Burnham's allies have suggested he would place responsibility for providing asylum accommodation on local authorities if he were to become Prime Minister by terminating multi-billion pound Home Office contracts with private companies housing migrants.
The Safe Transitions community guidance says: "People with asylum backgrounds are disproportionately represented within homelessness and rough sleeping services, often due to limited understanding of UK systems, fragmented transition support and barriers to accessing housing, welfare and local services."
The total value of the contract for developing the new guidance is almost £370,000.
Greater Manchester will also place refugees in homes as part of a "Refugee Lodging Scheme".
The scheme was established to prevent homelessness among refugees who only had 42 days to find an alternative to Home Office accommodation after being granted asylum.
More than 18,000 people have no permanent address in Greater Manchester, according to homelessness charity Shelter.
And in the borough of Manchester alone, more than 9,500 people are homeless, half of whom are children.
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Under the scheme, refugees are "matched" with "resident landlords" who will provide "support to access housing, benefits, employment, education, English language provision, health and community networks".
This contract is valued at more than £350,000.
Chris Philp, the shadow home secretary, told The Telegraph: "Andy Burnham has previously campaigned for immigrants to get benefits immediately upon arrival.
"Now we discover he is channelling hundreds of thousands of pounds to help recent immigrants, including illegal immigrants, to help themselves to taxpayer-funded benefits and housing.
"We are being crippled with huge taxes to fund welfare, and now Burnham wants to spend even more of our money on immigrants. This madness must end – but there is no chance Labour will do that, whoever their leader is."
The GMCA said the Safe Transitions programme was designed to provide preventative advice and support to migrants at risk of homelessness - avoiding the need for further expensive interventions.
This included providing some information sessions for people awaiting asylum decisions, after which they might have a short amount of time before being evicted from Home Office accommodation.
The GMCA said evaluations of the programme showed they saved more money than they cost, adding that the schemes are part of a £40million annual programme to combat homelessness and rough sleeping - which includes support for women, Armed Forces veterans, young people, former prisoners, refugees and asylum seekers.
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