The team was launched in 2010 by the same people who masterminded British Cycling's successes on the track at the 2008 Beijing Olympics with an ambition to produce the first British victor of the Tour de France by 2015.
The cycling team said Ineos would "continue to fund the current team in full, honouring all existing commitments to riders, staff and partners".
Sky's long-time team principal Dave Brailsford welcomed the move, saying "it ends the uncertainty around the team" and "represents a huge vote of confidence in our future".
"Today's announcement is great news for the team, for cycling fans, and for the sport more widely", said Brailsford.
The British-registered team had been seeking new funding after Sky announced in December it would end its ownership and sponsorship at the end of 2019.
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A report published past year by Britain's Digital, Culture, Media and Sport (DCMS) select committee accused Team Sky of crossing an "ethical line" by using permitted medications to improve the level of its riders - a claim Sky strongly refuted.
For those of you who don't follow professional cycling - I'd peg that at a solid 88 percent of the American public in the post-Lance Armstrong era - Team Sky is a top competitive team, with members winning the Tour de France six of the past seven years.
However, that success has not come without controversy.
The hugely successful team, founded in 2010 with the ambitious goal of securing a first Tour de France victory by a British cyclist within five years, have won eight Grand Tours since 2012.
"There are a lot of big names in that team who would potentially have had to look for new sponsors and there's limited places now with the amount of teams that have folded", Wiggins said on his Eurosport show.
"It's a harsh change of tone that may see Sky's Ocean Rescue campaign to clear plastic pollution from our oceans ditched from the team jersey in favour of INEOS - one of the biggest plastic producers in Europe".
Thomas, who beat Froome to Tour glory last July, added: "Super happy that the team can continue and stay together!" Froome's participation in the race was something of a surprise as he had been expected to focus on the Tour and a potential fifth crown, while he also raced in Italy under the cloud of a UCI investigation into a test result showing high levels of the anti-asthma drug salbutamol returned during La Vuelta.