Shares in DSV rose 8.3% by 0844 GMT to hit a record high.
"This is very positive news and exactly what has been at the top of investors' wish list," said Mikkel Emil Jensen, analyst at Sydbank.
"And it's exactly what DSV want more of, and where they are strongest in terms of earnings, so there is an opportunity to create really good synergies," he added.
Agility's logistics unit has around 17,000 employees and had revenue of $4 billion last year.
DSV's Chief Financial Officer Jens Lund told Reuters in an interview that the unit is "an excellent match" and that he expects to lift profitability at the Agility unit from a current operating margin of 3.5-4% to DSV's margin of around 10%. He declined to elaborate on how much synergy the acquisition will create.
"This will give us good exposure in Asia-Pacific and the Middle East," Lund said.
The acquisition will increase DSV's freight volumes by around a quarter and give it an extra 5% in global market share, according to Lund.
"This industry is still very fragmented," he said.
DSV has a strategy of growing via acquisitions and less than two years ago bought Swiss logistics group Panalpina for around $6 billion.
Under the Agility deal, DSV Panalpina will transfer 19.3 million new shares worth 1 Danish crown each to Agility, representing around 8% of its shares, making the Kuwait company the second largest shareholder in DSV.
DSV expects the Agility unit to be fully integrated around a year after the transaction closes in the third quarter.
DSV Panalpina also reported first-quarter operating profit above expectations on Tuesday and raised its expectations for full-year profit.
Its operating profit before special items stood at 3.07 billion crowns, topping the 2.70 billion expected by analysts for the January-March quarter in a poll gathered by the company.
DSV raised its forecast for annual operating profit before special items to 11.25 billion-12.0 billion crowns from 10.5 billion-11.5 billion.
($1 = 6.1614 Danish crowns)
(Reporting by Jacob Gronholt-Pedersen; additional reporting by Nikolaj Skydsgaard; editing by Sam Holmes, Jason Neely and Susan Fenton) ((firstname.lastname@example.org; +45 3274 2001; Reuters Messaging: email@example.com))