The compound noun repeat offender is recognised by the OED, as the below extract will confirm.
Nonetheless to describe someone as a "repeated offender" would also be idiomatic. But it would have a less-official sense, and be used more loosely, in conjecture, or to make a point.
Repeat offender is, inter alia an official categorisation of prisoners and people charged with crimes.
b. Forming compounds denoting a person who does something (implied by
the second element) again or repeatedly, as repeat customer, repeat
offender, repeat viewer, repeat visitor, etc.
1906 Pearson's Mag. July 108/2 It is your ‘repeat’ customers that
make your business profitable.
1940 Science 16 Aug. 143/2 An immense public, equivalent
numerically—not allowing for repeat visitors—to approximately four per
cent. of the total population of the entire nation.
1952 F. Pohl & C. M. Kornbluth in Galaxy June 33/2 Survey the
book-buyers, the repeat-viewers of O' Shea's TV shows.
1978 Washington Post 8 Aug. c4/5 Many juveniles, he adds, are
repeat offenders, ‘recycled’ through the system.
1986 A. Isserman Population Change & Econ. i. 16 Demographers have
noted that a large proportion of migrants are repeat migrants or
return migrants. 1993 Parents June 65/4 (heading) About 80% of
repeat miscarriers suffer from polycystic ovary syndrome.
2003 Philadelphia Inquirer 11 July a14/2 Judges could be ordering
repeat offenders to equip their vehicles with ignition switches that
work only when a driver proves his or her sobriety by blowing into a
tube.
