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.
“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.
Instead he thanked Cuba’s leaders and people and said he had confidence in his doctors.
“Onwards to victory!! We will live and we will overcome!!!” he wrote in his final tweet.
Local media quoted Vice-President Nicolas Maduro as saying that Mr Chavez landed at 02:30 local time (06:30 GMT) before being transferred to the Military Hospital in Caracas.
The extent of Mr Chavez’s illness is shrouded in mystery, but it is understood to be serious.
During his treatment the Venezuelan leader is reported to have had tumours removed from his pelvic region.
He has also undergone prior rounds of chemotherapy and radiation treatment.
Though there have been few details about the president’s exact treatment, Vice-President Nicolas Maduro described it as “extremely complex and tough”.
Mr Maduro has effectively been running Venezuela since Mr Chavez went to Cuba, and the opposition has demanded clarity about who is in charge.
Delaying the inauguration scheduled for 10 January, the Venezuelan Supreme Court ruled that Mr Chavez could be sworn in at a later date.
But the opposition argued that National Assembly Speaker Diosdado Cabello should take over and new elections should be held.
Reprinted from BBCnews