The Reds will receive a fee for the 19-year-old, with a further £2m ($2.5m) in performance-related add-ons forming part of the final deal.
There will also be a 20 per cent sell-on clause in the deal, as well as a buy-back option.
Having provisionally agreed terms on an extension in January, the Portuguese youth international was disappointed at not being allowed to leave on loan for the second half of the campaign.
Liverpool fielded a series of enquiries about him this summer, but Camacho rejected the chance to speak to Wolves, AC Milan and Schalke, concerned he would not get sufficient playing time at those clubs.
Lisbon-born, his preference was always to return to Sporting, who had agreed a loan deal with the Reds back in January only for Jurgen Klopp to veto the move. Had Liverpool allowed him to see out the remainder of his contract, they would have been due just £270,000 ($340,000) in compensation for a player who joined the club as a 16-year-old from Manchester City.
The ideal situation for the Reds would have been for Camacho to sign a new deal and then go out on loan, but discussions with his representatives proved fruitless, with the player keen to secure regular football in his home country.
Camacho impressed as part of Liverpool’s UEFA Youth League side last season, and made his Premier League debut as a late substitute in the win over Crystal Palace at Anfield in late January, three weeks after starting at Wolves in the cup.
Sources have told Goal that this move is not linked to reports suggesting Liverpool will make a move for Sporting midfielder Bruno Fernandes, and that the Reds have no interest in signing the 24-year-old despite persistent claims in the Portuguese media.
The Reds completed the signing of Sepp van den Berg from PEC Zwolle on Wednesday, in a deal worth an initial £1.3m ($1.6m).