 Kuzvarwa muTrieste, Cudicini akatanga basa rake rehunyanzvi neUdinese muna 1955, achiita kutanga kwake mumwaka wa195556 Serie B, uye akawana kukwidziridzwa kuSerie A nekirabhu. Mumwaka wake wekutanga muItaly yepamusoro, akaunganidza kuoneka gumi nematatu mumwaka wese, uye akacherekedza Serie A yake yekutanga neyakachena sheet mukukunda 20 kumba kuhwina Palermo musi wa 2 Zvita 1956. Muna 1958, akabatana neRoma. Mushure memwaka miviri semuchengeti wemagariro echikwata kumashure kwaLuciano Panetti, akasimudzirwa kuva muchengeti wemagariro echikwata muna 1960, uye akachengetedza chinzvimbo chemwaka mitanhatu inotevera, achiunganidza mitambo 166 yeligi, uye kuhwina Inter-Cities Fairs Cup muna 1960-61 uye Coppa Italia muna 1964. Akapedza mwaka wa1966-1967 Serie A neBrescia, achibatsira kirabhu kudzivirira kudzikiswa. Muna 1967, pazera remakore makumi matatu nemaviri, akabatana neMilan, kwaakagara kusvika pamudyandigere muna 1972, achiita 127 makwikwi emakwikwi ekirabhu uye 183 makwikwi mumakwikwi ese pasi pemaneja Nereo Rocco; akawana kubudirira kwakakosha mudzimba nekune dzimwe nyika nekirabhu, kuhwina mukombe weSerie A uye Mukombe weVakunda Mukombe mumwaka wake wekutanga, uchiteverwa neEuropean Cup neIntercontinental Cupmuna 1969, uye pakupedzisira Coppa Italia muna 1972. Ndiye muchengeti wechinomwe weMilan anovhara nguva dzose, achitevera Christian Abbiati 380, Sebastiano Rossi 330, Dida 302, Lorenzo Buffon 300, Enrico Albertosi 233, uye Dario Compiani 221. 