The Romania international moves to Celta as a free agent with his Venezia deal to expire at the end of the month.
Celta have announced Radu has agreed terms over a four-year deal.
The 28 year-old made 15 appearances in Serie A with Venezia last season, having also seen action with Bournemouth, Parma, Genoa and Inter Milan.
Radu also has four caps with Romania.