The 25-year-old earned his first Ireland 'A' caps during the 2006 Barclays Churchill Cup and also represented Ireland at the 2005 Sevens World Cup in Hong Kong. He scored 17 tries in 40 matches during his time with Ulster, but had limited game-time last season and has opted to join Edinburgh on a two-year contract subject to a medical.
Also capped for Ireland at Under-18, Under-19 and Under-21 levels, Maxwell said: "I'm looking forward to joining Edinburgh as there is a good buzz at the club and it seems to be moving forward. I have always liked the style of rugby they have played. It's funny the way it's worked out that I'm joining the team I scored against in my first and last games for Ulster."
Commenting on Maxwell's signing, Edinburgh head coach Lynn Howells said: ""Andrew has proved when he's played against us that he has pace and is a finisher. He's represented Ulster in both the league and in Europe on many occasions and so brings experience of playing at that level too. He's an out and out winger and has been a valued member of every squad he's played in."
Edinburgh have also today announced the signing of Scottish lock Craig Hamilton from Border Reivers.
Edinburgh chairman Alex Carruthers added: "Andrew is a recognised finisher. Last year, wing was a difficult area for us with injuries to Simon Webster and Chris Paterson, and given that both are likely to be at the World Cup, it is important for us to augment the squad.
"We had several options from overseas, but are delighted to offer Andrew the opportunity to continue his career in the Magners League and Heineken Cup and look forward to him scoring for us rather than against us."