Umbro provides kit for the England team as well as six Premier League clubs including West Ham, Everton and Blackburn.
Nike already provides Premiership kits for teams including Manchester United, Arsenal and Fulham. Since the early 1990s, Nike has grown its football revenues from about $40m to approximately $1.5bn.
Mark Parker, Nike president and chief executive, said: "Umbro is a brand with a powerful heritage and deep experience in the world's most popular sport and the world's biggest football market.
"With its close links to The Football Association and the England team, Umbro's future is even stronger than its past. We are fully committed to helping Umbro reach its full potential, and we are delighted that Umbro's board is unanimous in its support of our offer."
Brian Barwick, the chief executive of the Football Association, the organisation which oversees the England football team, said the body would benefit from Nike's "marketing expertise and financial strength".
Speculation had been rising that Nike was set to launch a bid for Umbro after the latter said last week that it had received an approach about a possible offer.
The news led to retailer JJB Sports, which is one of the main sellers of England football shirts, to buy a 10.1% stake in Umbro, in a move designed to protect its stake in the market for England football shirts.
However, recent sales of England replica tops have not met expectations, a situation that is set to worsen if the team fails, as expected, to qualify for Euro 2008, following its 2-1 defeat in Russia last week.
In addition to the England team, Umbro also provides kit for the Republic of Ireland, Northern Ireland, Norway and Sweden.
In Scotland, Umbro supplies kit to Rangers and Hearts. Rangers' arch enemy Celtic is kitted out by Nike, raising the prospect of both teams being supplied by the same kit manufacturer.
Last month, Umbro revised its 2007 profits forecast from £30m to just over £22m following a slump in sales of replica kits.
A decline from its strong performance in 2006 -- a World Cup year -- had been expected, but tough retail conditions, bad weather and a series of underwhelming performances by the England national team took their toll.
In August, Umbro hired Love to manage its global advertising account, which will see the agency maximise the brand's association with England stars Michael Owen and John Terry, and Portugal international Deco, ahead of Euro 2008.
The deal is consistent with recent Nike marketing activity, as the US sportswear company recently announced a new urban football initiative in the run-up to Euro 2008.
Nike is to launch a series of branded football events aimed at young people, with advertising created by Wieden + Kennedy and AKQA.