Hazard, 28, has been linked with a move from Chelsea to Real Madrid this summer -- admitting two weeks ago he'd told the club of his intentions -- and following the match he told BT Sport it was time for a "new challenge."
"We will decide in a few days and the only target in my mind was to win this final," Hazard said. "I have made my decision already and now I'm waiting on both clubs. I think it is a goodbye, but in football you never know.
"My dream was to play in the Premier League and I have done that for one of the biggest clubs so maybe now it is the time for a new challenge."
If Hazard does leave this summer, he'll do so with six titles to his credit during his seven seasons at Stamford Bridge, including two Premier League trophies, one FA Cup, one League Cup and two Europa League wins with the crown he helped Chelsea secure in Baku.
Chelsea and Arsenal both looked sluggish in the first half -- with the kickoff not taking place until 11 p.m. local time -- but Hazard helped the Blues find their form in the second half with a goal from the penalty spot and a sweet finish soon after to go along with his assist on Pedro's goal.
Hazard said of his team's effort after the break: "It was good. I think both teams were playing with a bit of stress with it being a final, but when Olivier [Giroud] scored it was the beginning of a great night.
"We played well and controlled the game and I'm happy to leave this trophy with the boys. The manager said to carry on playing football at the break and today we showed this mentality."
Hazard, 28, joined Chelsea from Lille in 2012 for £32 million. Real Madrid have not tried to hide their desire to sign the Hazard, with president Florentino Perez admitting this week that he has been chasing his signature for years and expects to land the Belgian this summer.
Following the match, manager Maurizio Sarri was also asked about Hazard's future and his own, with reports suggesting he may be in line to take up the coaching job at Juventus left vacated by the departure of Max Allegri.
"As you know, Hazard is a wonderful player, but you have to spend two or three months to understand him as a man," Sarri said. "But when you are able to understand him as a man, he's a wonderful man. I knew. I knew that Eden wanted to leave, of course. But, as I said in every press conference, I wanted to respect his decision.
"You know very well that I love the Premier League, the level of the competition. I am lucky because I am in Chelsea, one of the best teams, one of the best clubs in the Premier League in the best championship in the world. So, at the moment, I am happy.
"But, of course, I want to know if the club are happy. If we can improve. That's normal, I think. But I do a discussion with the owner, the president, the director after every season in every club, so I think it's normal."
Chelsea didn't lose during their Europa League campaign, winning 12 and drawing three, to become the first team to go unbeaten en route to a major European title since Manchester United did it in the 2007-08 Champions League.
And Sarri said his team were deserved winners: "I am really very happy, but I think the shirt is important. The front of the shirt. The trophy is very important for the club. Then is less important the back of the shirt, the name of the players and the name of the coach. Of course the trophy is very important for us because our feeling was we deserved to win.
"The Premier League is not easy to react in because the level is really very high. In the end we got into the Champions League through the Premier League - not easy. In the Europa League we played 15 matches and won 12 games, and drew three. So I think we deserved to win the Europa League.
"It's very important for me, but very important for us. I'm really very happy with my players. Something changed at the beginning of February. We lost 6-0 in Manchester against City, but we started something different. And so my feeling is we deserved to win."
ESPN FC's Chelsea correspondent Liam Twomey contributed to this story.