In three messages posted on Twitter, Mr Chavez, 58, thanked Cuban President and ex-leader Raul and Fidel Castro.
He also thanked Venezuelans for their support and said he would continue treatment in his home country.
He has been president for 14 years and was re-elected for another six-year term in October 2012, but his swearing-in was delayed because of his illness.
Mr Chavez went to Havana for surgery on 11 December, his fourth operation in an 18-month period for cancer first diagnosed in mid-2011.
Last week the first images of him since the operation were broadcast by Venezuela’s government.
He was pictured smiling as he lay in bed reading a newspaper, with his two daughters by his side.
Thanks and praise
Mr Chavez announced his return to Venezuela to his 3.9 million Twitter followers in a series of tweets that were bombastic in tone but short on detail.Hugo Chavez’s tweet was the first indication he had returned home
“We have arrived back in the land of Venezuela. Thank you Lord!! Thanks to my beloved people!! We will continue our treatment here.”
There was no information about when or why he returned, and no details about whether he would actively take up the duties of office.
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