Philippe Coutinho is set to fly to Barcelona to finalise his €160 million (£142m) move to the Catalan giants after Liverpool finally agreed an extraordinary deal to sell the Brazil international.

The fee is the biggest ever received by a British club – as well as the biggest ever paid by a Spanish one – and is the third-highest ever in the world after Neymar’s world record €222m (£197m) move to Paris Saint-Germain and the €180m (£160m) the French club are also paying for Kylian Mbappe.

Exclusively revealed by Telegraph Sport, the deal was agreed on Saturday afternoon after months of delicate negotiations, with Barcelona paying a significant portion of the money up-front and then a number of guaranteed add-ons. Importantly, it means Liverpool will eventually receive the full €160m.

A statement from Liverpool read: “Liverpool FC can confirm Philippe Coutinho will be leaving the club after a transfer agreement was reached with FC Barcelona, subject to medical and agreement of personal terms.

“The player now has permission to complete the usual formalities to conclude the transfer immediately.”

It is possible that Coutinho – who is set to sign a five-and-a-half-year deal with a €400m buy-out clause – will attend Barcelona’s match at the Nou Camp against Levante on Sunday afternoon. If everything goes smoothly, the 25 year-old could then train with his new team-mates on Monday and even be available to make his Barca debut in the Copa del Rey against Celta Vigo on Thursday evening.

Earlier, Coutinho withdrew from the Liverpool squad that is heading to Dubai for a few days’ break after their FA Cup victory over Everton on Friday evening, for which he was officially injured.

The astonishing deal concludes a long-running transfer saga, with the Brazilian having hoped he would move to Barcelona last summer following Neymar’s departure. At the time, Liverpool refused to sell with owners Fenway Sports Group taking the unusual step of releasing a statement declaring that the player would not be allowed to go in that transfer window.

Since then, though, Liverpool have softened their stance and negotiations have been helped by the understanding approach taken by Coutinho’s representative, Kia Joorabchian, who has been heavily involved throughout the talks.

Relations between all parties, therefore, remained amicable and it is regarded as a good deal for everyone involved with Liverpool reasoning that the impact made by Mohamed Salah, and the form of other players such as Sadio Mane and Roberto Firmino – plus the return to fitness of Adam Lallana – has made them less dependent on Coutinho.

The club also accepts that it is Coutinho’s dream to move to Barcelona and, ultimately, they did not want to stand in his way, especially as they have reached a price – and the terms – they deem acceptable.

Nevertheless, Liverpool had hoped to persuade Coutinho to remain until the end of this season, especially as he cannot play Champions League football for Barcelona, and with both clubs in the last 16, but he was determined to go as soon as possible.

As also revealed by Telegraph Sport, Liverpool spent a world-record fee for a defender recently when they signed Virgil van Dijk – who made his match-winning debut against Everton – from Southampton for £75m.

However, Liverpool did not have to sell Coutinho to ‘balance the books’ and they will target a replacement for their playmaker. It remains to be seen, though, whether that can be done during this window.

They attempted to sign Monaco’s Thomas Lemar last summer but were out-bid by Arsenal, although the France international eventually opted to stay with Monaco. It is understood that he would be interested in moving to Liverpool – and Arsenal also retain a strong interest, especially if they sell Alexis Sanchez to Manchester City – but Monaco are insisting they will not let him go before the end of the season. They fear they will miss out on qualifying for Champions League football if they do.

Reports in France have linked Liverpool with a move for Leicester City’s Riyad Mahrez, but this has been strongly rejected by senior sources at Anfield who say they have no interest in the Algerian international.