The Portuguese teenager, who is understood to have signed a five-year contract, will officially join on July 1st.
Carvalho, out of contract this summer, was set for a move four months ago on deadline day when a £5million deal was agreed with the SkyBet Championship winners but the transfer window closed without a medical and formal paperwork being concluded.
However, with a number of overseas clubs starting to show interest post-January it is understood that Liverpool were keen to avoid being dragged into an auction for the player when his contract expired.
Therefore they subsequently agreed that in addition to the initial fee they would pay a further £2.7m in add-ons and attach a 20 per cent sell-on clause to secure the player’s future ahead of the end of the season.
Those terms mirror the ones set by a tribunal over the signing of another Cottagers youngster Harvey Elliott in the summer of 2019, a transfer which was much more acrimonious.
The strained relationship between the two clubs as a result of that deal was improved by the transfer Harry Wilson to Craven Cottage last summer and Liverpool were impressed with the cooperation they received from Fulham’s owner Tony Khan and chief executive Alistair Mackintosh during the Carvalho negotiations.
That led to Fulham granting Carvalho, who scored 10 goals in 36 league matches this season, permission to visit Liverpool’s AXA training complex to meet manager Jurgen Klopp and his coaching staff, have his medical and agree personal terms.
Klopp is understood to highly value the player’s versatility, skill set and personality and his status as a home-grown player due his development at Craven Cottage is an important factor as Liverpool look to freshen up an ageing squad.