Supporters feared the pair would be sold to help service debts of almost 400 million pounds but chairman Martin Broughton assured the former Fulham boss he would not have to get rid of anyone.
GEAR:Get the new Liverpool shirt
"Players are not for sale," Broughton told a news conference. "We don't need the money and we don't have to sell them because of the debt."
The much-travelled Hodgson has been tasked with reviving Liverpool's fortunes after the 18-times English champions decided last month to end Spaniard Rafa Benitez's six-year reign.
Vastly experienced, the 62-year-old takes over after a woeful season for the Anfield club who finished seventh in the Premier League and missed out on qualifying for the lucrative Champions League.
"This is the biggest job in club football and I'm honoured to be taking on the role of manager of Britain's most successful football club," said Hodgson after signing a three-year contract.
"I'd like to think I've earned this job. My career shows that kudos is not something I've actively sought but this job carries that with it, and enormous responsibility, and I'm ready to take it on."
Hodgson, whose name has been linked to the England job since their World Cup second-round exit on Sunday, becomes Liverpool's 18th manager and the first Englishman to hold the post since Roy Evans left in 1998.
"I'm convinced the chance to work here is the right thing for me in my career," said the Londoner. "I'm here on merit.
KEY PLAYERS
"I'm anxious to meet two key players (Gerrard and England defender Jamie Carragher) and hear how they feel about the club. I took the job because I wanted to be manager and work with the players, benefit from the fan base and incredible support.
"Each club has it's problems and issues and as a coach you are expected to sort them out. I can't deny it's not an easy one," added Hodgson who is not allowed to sign Fulham players as part of his severance deal with the London club.
Hodgson has gained a reputation as an astute tactician after an odyssey that has taken in 12 clubs in six countries during his 34-year coaching career.
As well as spells in club football in Denmark, Norway and Sweden, where he won five league titles with Malmo, multi-lingual Hodgson also managed Switzerland and qualified them for Euro 1996.
Last season he was named Manager of the Year in England after leading modest Fulham to the Europa League final where they lost to Atletico Madrid.
"The club would like to wish Roy the very best for the future and thank him for all that was achieved during his tenure," Fulham said in a statement.
