Silvio Berlusconi's wealth helped make AC Milan one of Europe's most successful clubs. Photo: AFP
In a joint statement, the clubs said that the first edition of the Silvio Berlusconi Trophy would be held at Monza's U-Power Stadium on August 8, with the match switching venues each year.
"The initiative aims to honour and keep alive the memory of president Silvio Berlusconi, who wrote indelible pages in both clubs' histories," the clubs said.
Former Italian prime minister and media mogul Berlusconi, who died last month aged 86, was an extremely divisive figure in the country's political and cultural spheres.
But his enormous success as a club owner earned him the admiration of legions of fans.
He reigned supreme at Milan from 1986 until 2017, buying an ailing club on the brink of bankruptcy and turning them into titans of the European game.
During his time at the San Siro Milan won 29 trophies, including five Champions League and eight Serie A titles.
After selling Milan for 740 million euros he picked up Monza, then in the third tier, for a relative song in 2018 through his holding company Fininvest and alongside long-time ally Adriano Galliani took them up to Serie A.
Monza finished 11th last season, their first ever in the top flight of Italian football, but Berlusconi's death has led to speculation that Fininvest could sell the club.
On Thursday Berlusconi's eldest son Pier Silvio said "we children will find a way to best keep dad's dream alive", adding that Galliani would be "at the centre" of the club's future.
Sources told AFP on Thursday that Pier Silvio and his sister Marina Berlusconi would take joint control of Fininvest following the reading of his will.
The pair, who are children of Silvio Berlusconi's first wife Carla Dall'Oglio and until now held 7.65 percent in Finivest, will according to the source increase their joint stake to 53 percent.
Marina Berlusconi has since 2005 been president of Fininvest, which controls a myriad of companies including the MediaForEurope (ex-Mediaset) television group, Mondadori publishing house and the Mediolanum bank.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)