The Ireland goalkeeper has continued to earn add-on benefits for his childhood club, with the initial €500,000 deal improved by the activation of a clause for senior competitive international appearances, which generated another high six-figure sum.
Completion of the Southampton deal would put Rovers in line for a dividend in the ballpark of €2m which makes the 20-year-old by far the most lucrative export in the history of the league.
Bazunu retains a strong connection with the Hoops, and has been a visible presence at both their games and the training ground on his summer break. His family are season ticket holders at Tallaght.
A host of English and European clubs were interested in a move for his services off the back of a successful loan spell at Portsmouth.
Everton made a formal enquiry with City but while they and other clubs mulled over their options, Southampton came forward with a willingness to meet a valuation.
They had a vacancy to fill with Fraser Forster departing for Tottenham, and Bazunu will battle with the number one spot for Alex McCarthy.
As reported last month, there will be a buyback option in the deal which gives City the chance to bring Bazunu back to the club down the line.
He is highly rated by all involved with City, but his path to first team action was blocked by the excellent Ederson.