The 18-times English champions were taken over by New England Sports Ventures (NESV) for 300 million pounds after a Texan court lifted a restraining order designed to prevent the sale.
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"It's a very good day for the club," Hodgson told a packed news conference at the club's training ground shortly before the deal was officially confirmed.
"It's a relief... it's been a very difficult couple of weeks... we've had to live through that bad time.
"There's no doubt a cloud has been lifted from the football club today."
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"We didn't talk about investment but that said, the mere fact that the club will be taken over and the debts wiped off immediately puts us into a very different financial position to the one we've been in," he said.
"The sort of money we would have to pay the bank in interest can now possibly be made available for players and if that money alone was made available we'd be quite wealthy."
'NO FEARS'
"No doubt the players will be able to get on now with playing football without having to any questions to answer or having any fears," he said.
"It would be naive to say these things (takeover issues) don't matter. When club in a bad situation it is bound to affect you in some way." He said news of the takeover was coming at the right time ahead of Sunday's Merseyside derby at Everton, in which the club would be looking to kickstart its season.
"The derby match comes at a good time," said Hodgson, whose team suffered an embarrassing 2-1 home defeat by Blackpool in their last league match two weeks ago.
"We've had two weeks to chew and to savour that defeat. Having a game of the quality and magnitude - in a derby against our fiercest rivals - that is an ideal way to bounce back if we are capable of doing so. I think we'll b
