Hayward Tyler submitted outline plans for the firm's seven-acre site at 1 Kimpton Road, as it aims to relocate in the town.
The triangular brownfield site lies between the Midland Mainline railway and the Luton and Dunstable Busway.
"Hayward Tyler has had a presence in Luton for more than 150 years," according to a report to the borough council's development control committee.
"It operates a global business, and designs, manufactures and services electric motors and pumps," said the report.
The proposals also involve "demolishing buildings associated with the manufacture and servicing of the company’s products."
Affordable housing will account for about 200 of these homes, added the report.
One in ten would be studio apartments, a third are one-bedroom flats, 37 per cent two-bed and the remainder three-bedroom properties, with 709 parking spaces and storage for 1,000 bicycles.
Planning team leader Clive Inwards said: "There's limited harm to the listed buildings.
"The scale of the tallest elements of the scheme have been reduced during the application process from 21 stories down to a maximum of 16 primarily to address concerns of the impact on Luton Hoo.
"The proposal is promoting a genuinely mix-use scheme.
"It could support about 370 jobs, as well as retaining 150 associated with the applicant's business."
Highways development manager John Maple said: "The internal site layout may change radically, as it's not being developed by the applicant.
"I expect to see an entirely different scheme come forward."
A statement from applicant Hayward Tyler's agent said: "This application proposes to redevelop the company's premises on Kimpton Road to enable it to relocate to a more suitable site in Luton.
"The relocation would help increase efficiencies in the production process and ensure the firm continues to compete in the global market.
"The business is committed to remaining in the borough in the long-term.
"The redevelopment is dependent on the firm securing an alternative site locally. A number of options are being considered.
"There's an opportunity to secure a health facility on site, if this is required.
"It could link up other developments along Kimpton Road, such as Napier Park and Power Court, and complete a pedestrian link from Luton Parkway Station to Luton Station and the town centre."
Labour Round Green councillor Mark Rivers: "It would be nice to provide a pedestrian link under Crawley Green Road, at that point, which joins up Power Court and this new development.
"That would require some expensive civil engineering."
Labour Farley councillor Dave Taylor, who chairs the committee, replied: "That could be considered later on in the planning process."
The CCG, which would fund it, has to decide whether it wants to put a medical centre on the site, he explained.
Conservative Bramingham councillor Gilbert Campbell said: "My concern is 100 studio, 330 one-bed, so 430 small units.
"We could have more than 2,000 people living in that block. It's too many. It's a high density development."
Labour Farley councillor Mahmood Hussain agreed, saying: "It's trying to cramp so much into a very small area.
"But overall I support this because affordable housing is desperately needed in the town centre and the employment stays in Luton."
Councillors approved the scheme with nine in favour and one against.