He has signed a three-year deal with the Italians worth £5m a year — compared to the annual £15m he was getting at Spurs.
But as part of his severance, the North Londoners agreed to pay him the shortfall in salary if he took another post on lower wages before the end of his contract next summer.
That means when Mourinho takes over at the Stadio Olimpico this summer he will receive £5m from Roma and, for next season only, £10m from Tottenham.
But Spurs have saved £5m on what they would have paid him had he not accepted another job.
The ex-Porto, Chelsea, Inter, Real Madrid and Manchester United boss is keen to show he is not at fault nor been affected by his shock departure after just 17 months in charge.
Mourinho, 58, will replace fellow Portuguese Paulo Fonseca.
He said: “The incredible passion of the Roma fans convinced me to accept the job and I cannot wait to start next season.”
Spurs chairman Daniel Levy and his players and staff knew nothing of Mourinho’s new job until it was announced on TV yesterday afternoon.