But the business, which accounts for about a third of Motorola Solutions' total revenue, has been struggling as companies delay orders and cut spending.
After the sale, Motorola Solutions will be left with its core government and public safety business. It also plans to retain its iDEN products portfolio, which is a part of its enterprise business.
"Upon closing of the transaction, we intend to return the proceeds to our shareholders in a timely fashion," Motorola Solutions Chief Executive Greg Brown said in a statement.
Zebra's shares were up about 6 percent at $72.45 before the bell, while Motorola Solutions' stock was up 3.5 percent at $66.01.
"It's an aggressive play by Zebra to fortify their position in the entire AIDC (automatic identification and data capture) space," Northcoast Research analyst Keith Housum said.
The acquisition will be funded through a combination of $200 million cash on hand and $3.25 billion debt, comprising a credit facility and issuance of debt securities.
Morgan Stanley, the financial adviser to Zebra, is providing a financing commitment for the debt.
Zebra said it expected the deal to add to earnings immediately after closing at the end of this year. About 4,500 Motorola Solutions' employees will join Zebra.