The acquisition is expected to be completed by the end of 2024 subject to clearances and approvals by competition and foreign investment law authorities in various jurisdictions.
Liberty will not be the first company to own both Formula One and MotoGP.
Private equity firm CVC Capital Partners had owned both F1 and MotoGP but was forced to sell the motorcycle series to buy F1 after EU competition regulators raised objections.
"Liberty Media Corporation has announced an agreement to acquire MotoGP. MotoGP is the pinnacle of two wheels," read a statement issued by MotoGP.
"Liberty Media will acquire approximately 86 percent of Dorna, with Dorna management retaining approximately 14 percent of their equity in the business.
"The transaction reflects an enterprise value for Dorna/MotoGP of €4.2 billion (£3.59bn) and an equity value of €3.5 billion (£2.99bn), with MotoGP's existing debt balance expected to remain in place after close."
Long serving CEO Carmelo Ezpeleta will remain in the post he has occupied since 1994 with the business headquarters remaining in Madrid.
"We are thrilled to expand our portfolio of leading live sports and entertainment assets with the acquisition of MotoGP," said Greg Maffei, Liberty Media President and CEO.
"MotoGP is a global league with a loyal, enthusiastic fan base, captivating racing and a highly cash flow generative financial profile. Carmelo and his management team have built a great sporting spectacle that we can expand to a wider global audience."
Ezpeleta said he was looking forward to the 21 race global championship evolving even further.
"This is the perfect next step in the evolution of MotoGP, and we are excited for what this milestone brings to Dorna, the MotoGP paddock and racing fans," said Ezpeleta.
"We are proud of the global sport we've grown, and this transaction is a testament to the value of the sport today and its growth potential.
"Liberty has an incredible track record in developing sports assets and we could not wish for a better partner to expand MotoGP’s fanbase around the world."
