Cyclins A2 and E1 regulate the cell cycle by promoting S phase entry and progression. Here, we identify a hepatocellular carcinoma (HCC) subgroup exhibiting cyclin activation through various mechanisms including hepatitis B virus (HBV) and adeno-associated virus type 2 (AAV2) insertions, enhancer hijacking and recurrent CCNA2 fusions. Cyclin A2 or E1 alterations define a homogenous entity of aggressive HCC, mostly developed in non-cirrhotic patients, characterized by a transcriptional activation of E2F and ATR pathways and a high frequency of RB1 and PTEN inactivation. Cyclin-driven HCC display a unique signature of structural rearrangements with hundreds of tandem duplications and templated insertions frequently activating TERT promoter. These rearrangements, strongly enriched in early-replicated active chromatin regions, are consistent with a break-induced replication mechanism. Pan-cancer analysis reveals a similar signature in BRCA1-mutated breast and ovarian cancers. Together, this analysis reveals a new poor prognosis HCC entity and a rearrangement signature related to replication stress.