The buyers include China's Apex Technology, which makes ink cartridge chips, and PAG Asia Capital, one of Asia's largest private equity firms.
The deal is yet to be cleared by the US Committee on Foreign Investment in the United States (CFIUS).
Like its competitors, Lexmark has been struggling as more firms move to a digital workplace.
The deal was sealed at a board meeting following an "exhaustive" review of alternatives, the company said.
Paul Rooke, chief executive of Lexmark, said the takeover would allow it to "reach the next level of growth and innovation" faster than as a standalone company.
"With the consortium's resources, we will be able to continue to invest in and grow the business to more fully penetrate the Asia-Pacific market for hardware, software and managed print services," he added.
Apex Technology chairman Jackson Wang said Lexmark would be a "tremendous cultural fit" with his own company.
The deal is expected to close in the second half of the year if it is approved by regulators. The CFIUS will review it to ensure it does not compromise national security.
Lexmark will remain headquartered in Lexington, Kentucky.
US printer manufacturer Lexmark is being bought by a Chinese-led group for $3.6bn (£2.5bn).