Benitez signed a new deal through to 2014 on Wednesday, ending months of speculation over his Anfield future.
"I was never worried because I know Rafa really wanted to stay at Liverpool and we wanted him to stay," Hicks told BBC Five Live Sport. "We agreed the economics some time ago and I'm glad we finally got it done."
Benitez fell out with Hicks and fellow American owner George Gillett shortly after they bought the club in 2007 after publicly criticising the club's transfer policy.
Hicks denied that the reason Benitez had taken so long to sign a new contract was that he wanted full control over the signing of players.
"Rafa was never wanting control of the transfer policy, he just wanted to make sure we had better decision-making capability and that we moved quicker than we had in the past," Hicks said.
"Rafa will make the recommendations but in English football it's very important that the chief executive should make the financial decisions not the manager."
ALWAYS BACKED
In a separate interview on Sky Sports News, Hicks said they had always backed Benitez's judgement in the transfer market.
"If you look back over the last few years we followed his recommendation, we signed Fernando Torres when he recommended him, we extended Pepe Reina's contract, we signed (Ryan) Babel, (Yossi) Benayoun, (martin) Skrtel, (Javier) Mascherano, (Andrea) Dossena, we even signed Robbie Keane but that didn't work out."
"Rafa is a professional and he knows he has operate to a budget and the budget will be set every year based on revenues and when we get a new stadium we will have higher revenues," Hicks said, adding that his rift with Gillett was over.
He also said he was confident the club's new stadium would be built once the global economic credit crisis had eased.
"The reality is we had to design and re-design the new stadium and didn't get out approvals from the council until September 18 last year," he said. "Then by October the global credit meltdown had already started.
"I'm hesitant to pick a date because I can't predict the capital markets but it's important the fans know it's still very much something we plan to do and we work on it every week. It has not been mothballed, it's going to happen."
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