McAndrew, the 29-year-old Australian pace-bowling allrounder, will be available from April until July to play in the LV= Insurance County Championship and T20 Vitality Blast.
"I can't wait to get to England to play with Sussex," McAndrew said. "I thoroughly enjoyed my time in county cricket last year and I am looking forward to taking the next step in my career playing red- and white-ball cricket this season. I look forward to teaming back up with Paul Farbrace and contributing to Sussex's success."
McAndrew featured for Sydney Thunder during his eighth BBL season, taking 13 wickets in the group stages to help them qualify for the play-offs. He delivered career-best T20 bowling figures of 4 for 32 against Brisbane Heat, three of those wickets coming in the final over to save the game for his side.
"In four-day cricket he runs in all day. His experience in England last year will pay dividends as his performances got better and better. It shows he can adapt and is willing to learn and coupled with a bowling engine, I am sure Nathan will be successful at Sussex."
Sussex won just one Championship match last year, finishing above only Leicestershire on the Division Two table, and they ended up seventh in the Blast's nine-team South Group.