The arrival of van Dijk is a huge step towards finally rectifying that and the fact that City and United were said to be interested is another win for Klopp.
Liverpool issued an apology to Southampton over the incident and the deal has been revived, with Van Dijk signing a contract for an undisclosed length of time that commences from January 1.
The 26 year old defender will move to Anfield in the New Year with British media reporting the deal to be worth $140 million.
"Delighted and honoured to have agreed to become a Liverpool FC player!" he wrote.
Liverpool have reportedly had an astonishing £75m bid accepted by Southampton for wantaway centre-back Virgil van Dijk.
The transfer saga dates back to the summer when the Saints reported Liverpool to the FA for "tapping up" the Dutchman, effectively ending their chances of signing him.
"I can't wait to pull on the famous red shirt for the first time in front of the Kop and will give everything I have to try and help this great club achieve something special in the years to come", he said.
A statement on the club's website read, "Liverpool Football Club can confirm they have reached an agreement with Southampton for the transfer of Virgil van Dijk".
Many Saints fans will be disappointed to let yet another top player slip through their fingers to Liverpool - following the departures of Sadio Mane, Dejan Lovren, Nathaniel Clyne, Adam Lallana and the now-retired Rickie Lambert.
It ends a long chase for the side now lying fourth in the Premier League.
Former Liverpool player Collymore is staggered at the fee.