Liberty Media Corp, run by rival media mogul John Malone, will take DirecTV in return for its 16.3% stake in News Corp, $550m in cash and three regional sports networks.
The long-time adversaries have been negotiating an agreement since Malone bought the shares in News Corp two years ago - challenging Murdoch's control of his own conglomerate.
The Federal Communications Commission yesterday gave the green light to the deal, though with conditions to protect competition. They cover programme access, programme carriage and various other measures.
It concluded that "the public interest benefits of the [deal] outweighed the potential harms" despite some commission members' reservations.
Democrat Michael Copps said: "This transaction is hardly an occasion to jump for joy. The commission should be waging a proactive battle against harmful media consolidation, not simply accepting small levels of deconsolidation when it comes."
Jonathan Adelstein, also a Democrat, wanted a condition to protect local content but was refused by his fellow members.
DirecTV said in a statement: "We welcome Liberty Media as our largest shareholder and we look forward to breaking ground on this exciting new chapter at DirecTV."