The Spanish carrier said it would make a capital gain of €47 million from the transaction.
Hispasat’s largest shareholder, Abertis, paid €68 million for the 7.2% holding, giving it an overall stake of 40.6%.
"This acquisition reinforces Abertis’ willingness to grow in the satellite infrastructure sector in those projects in which it can assume an industrial leadership role, while at the same time it demonstrates its capacity to reinvest in attractive projects with upside.” The company said in a statement.
Eutelsat is expected to pay €56 million for the remaining 5.8% stake, subject to regulatory approval.
The move is the latest in a series of asset sales by Telefónica as it looks to cut its debt.
Previous deals include the sale of its call centre business Atento, part of its stake in China Unicom and a listing of Telefónica Germany.
The carrier said it expects to have reduced its debt in 2012 from €56 billion to €50 billion as a result.
Telefónica had originally planned to sell its entire stake in Hispasat to Abertis, having reached an agreement with the company in February 2012 worth €124 million.
Eutelsat blocked the deal by exercising its right of refusal.