Lukasz Fabianski signed a four-year contract with Swansea City on a free transfer.
Fabianski, 29, has failed to pip Wojciech Szczesny for the starting role at the Emirates, and rejected a new contract to pursue first team football.
"The main reason I came to Swansea was because I want to be the number one goalkeeper," Fabianski said.
"It's going to be a real fight, but I'm not afraid of that. Competition is always good, so I think everyone will take positives from that.
The 29-year-old's seven-year spell with the Gunners concluded on a high as he played an integral role in an Arsenal's FA Cup triumph against Hull City at Wembley.
The Polish international, who joined Arsenal from Legia Warsaw in 2007, made one league appearance this season; the final game against Norwich.
Swansea manager, Garry Monk, believes Fabianski's arrival will present a healthy competition at the goalkeeper position.
“I hope we can help him [Fabianski] progress as a player and in his career, because at 29 he has got to the age where he wants a new challenge. Michel Vorm and Gerhard Tremmel will provide him with plenty of competition, but that's exactly what I want," Monk said.
“My job is to get the squad as competitive as possible across all areas and this signing confirms that thought process. It has to be a competitive environment and whoever backs themselves and comes out on top will wear the shirt.”
Monk, however, believes that Fabianski possesses the hunger that he demands in his squad.
"Speaking to him [Fabianski] this week I could see the hunger he has to come here and prove he is a number one goalkeeper. That's a great attitude to have and it's the only type of player I want at Swansea City," Monk added.
Fabianski is Monk's first signing since being appointed full-time manager at the Liberty Stadium, and the 29-year-old will join the club on July 1.