The council wants to move its current facilities on Doughty Road and Gilbey Road and officers at the authority will now consider potential locations.
The move to one site would also release the land at Doughty Road, which is identified for housing and economic development under the recently adopted local plan.
The site currently accommodates such council services as highway maintenance, security services and clinical waste collection.
But North East Lincolnshire Council has said that the site is “no longer fit for purpose” due to its condition and staff facilities which the authority deems to fall below its standards.
The authority added that the condition of the Gilbey Road building is poor and is restricted by the surrounding land which is owned by Associated British Ports.
Members of the council’s cabinet also approved the creation of a satellite site in the borough for a new community recycling facility.
Currently, Gilbey Road and a site in Immingham are used as community recycling centres.
Councillor Matthew Patrick, portfolio holder for environment, transport and energy, said that the report was “long overdue” on the sites.
“It’s clear that the depots that we have are somewhat showing their age,” he said.
“The plan will result in savings made on revenue costs and new commercial opportunities.
“We need to get moving and make sure we are fit for the 21st century.”
Meanwhile, council leader Councillor Ray Oxby said that the plan would be an opportunity to further regenerate Grimsby town centre.
“This site has long been identified as an area for redevelopment,” he said.
“The business case will be welcomed once we get it.”
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The Home Office has told RAF Scampton residents that they will not be notified when asylum seekers are moved onto the former airbase in order to avoid public pushback.
At a public engagement meeting for vulnerable people held at the Lincolnshire Showground on Thursday, it was conveyed to attendees that the timing of the migrants’ relocation will be kept undisclosed, due to concerns about potential public pushback.
Residents of Langworth, West Lindsey, continue to grapple with the aftermath of last month’s flood, which has left some without a place to stay and forced many to discard a significant amount of their possessions.
Several locals have resorted to hiring skips to dispose of damp and damaged belongings in the wake of the flood that struck on October 20, due to intense rainfall from Storm Babet.