The consortium includes UK-based Apax Partners, U.S.-based Warburg Pincus and Canada Pension Plan Investment Board (CPPIB) and Ontario Teachers' Pension Plan Board.
Inmarsat shareholders will get $7.21 cash, or 546 pence per share. Inmarsat's shares were up 8.5 percent at 549 pence by 0910 GMT, just above the offer price.
A takeover of the company could be closely scrutinized by the British authorities because of Inmarsat's position as a strategic asset.
The company was the first international satellite operator to be privatized, and Apax was part of the group that invested in 2003, before taking it public two years later.
The offer comprises cash of $7.09 for each share plus a previously agreed final dividend of $0.12 per share, representing a nearly 45 percent premium to Inmarsat's close on Feb. 27, a day before media reports said EchoStar was expected to renew its interest in the company.
Inmarsat is a long established provider of communication services to shipping and sees a growing opportunity to supply in-flight broadband services to commercial aircraft.
TOP SHAREHOLDER SUPPORT
The consortium said it received support from Inmarsat's top shareholder Lansdowne Partners, which holds about an 11.4 percent stake in the company.
The consortium's approach, which was made on Jan. 31 but disclosed only last week, comes after Inmarsat rebuffed a $3.25 billion cash and stock bid from EchoStar last summer.
Colorado-based EchoStar had proposed a cash and stock offer of 265 pence in cash and 0.0777 EchoStar shares for every Inmarsat share held, which valued Inmarsat at about 532 pence-a-share at the time.
Inmarsat had argued it "very significantly undervalued" the company and its standalone prospects and EchoStar dropped the bid last July.
Inmarsat said its directors consider the terms of the latest deal to be "fair and reasonable" and intends to unanimously recommend that shareholders vote in favor of the deal.
Inmarsat has been investing heavily in its networks, particularly focusing on in-flight connectivity, and as a result cut its dividend last year.
The stock has struggled in recent years as revenue in its maritime business - which is responsible for 41 percent of its total - has been eroded by competitors.
Inmarsat sees capital expenses moderating after 2020, which it hopes will boost cashflow. It also expects significant growth in markets including aviation and providing communications to the government.
Inmarsat was advised by J.P. Morgan Cazenove, PJT Partners and Credit Suisse on the financial terms.
(Reporting by Justin George Varghese in Bengaluru; Editing by Bernard Orr/Keith Weir)