The deal will allow Zebra, whose products help companies such as Amazon track inventory and supply chains, to tap the opportunity presented by the profusion of devices, ranging from cars to smoke alarms, connected to the Internet.
Motorola Solutions' enterprise clients include Wal-Mart Stores and TNT Express.
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.
In October, Zebra launched Zatar, a Web-based software that allows companies to deploy and manage devices and sensors connected to the Internet, also called the "Internet of things."
Zebra acquired Hart Systems, which provides Web-based inventory management software to the retail industry, in December.
Global merger and acquisition activity has surged this year, mainly in the technology industry. Deals worth about $618.4 billion have been completed, with a third of those in the technology, media and telecom sector, according to Thomson Reuters data.
Motorola Solutions estimated its quarterly results below analysts' expectations, saying volumes in its North America government business were lower than expected and some orders in its enterprise business were delayed.
The company estimated an adjusted profit of 50 cents per share and sales of about $1.8 billion for the first quarter ended March.
Analysts on average were expecting a profit of 51 cents per share on revenue of $1.88 billion, according to Thomson Reuters I/B/E/S.
Zebra estimated an adjusted profit of 88-91 cents per share and sales of $287 million-$289 million for the first quarter.
Analysts on average were expecting adjusted earnings of 83 cents per share on sales of $281.6 million.