Liverpool completed the double deal to land Spanish duo Alvaro Arbeloa and Francisco Manuel Duran before the closure of the transfer window.
Deportivo La Coruna right-back Arbeloa is believed to have cost the Reds £2.5million, while Duran has been signed on a free transfer as the teenager did not have a professional contact with Spanish second division side Malaga.
Arbeloa, 24, joined Depor from Real Madrid last summer and admitted his surprise that a move to Anfield materialised so quickly.
"Until Tuesday I wasn't sure whether I was going to leave or not," Arbeloa told the club's official website.
"My agent told me the deal was very advanced and I was then told that the deal had been reached between both clubs.
"For me this is a beautiful challenge and I hope everything goes well. It's a huge leap for me."
Meanwhile, Duran is relishing the prospect of working under Reds boss Rafael Benitez.
"It's a unique opportunity and I couldn't let it go by," he added.
"I have spoken with Rafa Benitez and I believe that this is the best option for me.
"To play for Liverpool is a dream for me and now I only desire to fight to play finally for the club."