Tramonte, 64, was the subject of a European arrest warrant after fleeing an Italian life jail term for an attack on a trade union rally in the northern city of Brescia.
The Italian court of appeal had on Tuesday confirmed his life sentence, ending a long-running legal case comprising a succession of trials stemming from the attack.
Portuguese police said Tramonte, a former secret service informant who was active in a far-right group, was run to ground in the central city of Fatima.
Tramonte, earlier acquitted, was finally sentenced two years ago for the Brescia blast, alongside fellow neo-fascist Carlo Maria Maggi.
The bombing was one of a clutch of terror attacks by hard right and left groups in Italy across more than a decade from the late 1960s.
Italians dubbed that period of violent turmoil, which saw hundreds of killings, the “Years of Lead”.
The Brescia attack was one of the worst in that troubled period along with the Piazza Fontana bombing in Milan in 1969 which killed 16 and the Bologna railway station blast which left 85 dead in 1980.