The Switzerland international is out of contract in July and he is ready to leave Turin after seven years there.
Arsenal have been in talks with the 34-year-old for the past few weeks and, according to Gazzetta dello Sport, a deal is now done.
Lichtsteiner is set to join Arsenal on a one-year contract, with the option to extend his stay by a further 12 months.
The right-back is said to have had offers to stay in Italy, as well as from clubs in China.