The United States international also had a stint with David Moyes's squad two seasons ago and said he was excited to be back at Goodison Park.
"Last time there was zero expectation," Donovan told the club's website on Friday. "Now I know there is some level of expectation but that's something all footballers deal with, it's part of the job.
"I don't worry about that, I just want to enjoy my two months here. I think I can help the team."
Donovan's last stint with Everton was a success after he played in 13 games, including 11 starts, and won the player of the month accolade for his performances in January 2010.
"I feel I've improved as a player since my time here before. Since then I've played in the 2010 World Cup and had another couple of years' experience," said the 29-year-old, who won the Major League Soccer championship title with the Galaxy last month.
Donovan, who is unlikely to feature in 10th-placed Everton's league game at West Bromwich Albion on Sunday, said the club treated him well in his previous spell at Goodison.
"The minute I stepped off the plane two years ago and watched Everton's FA Cup game with Carlisle United I felt wanted, I felt respected and that resonates and stays with you," he explained.
"It feels like coming home and it feels like family. It's an easy place to come to.
"From the kit man to the media people everyone is friendly and happy and they're excited to be a part of this club. It's infectious. I almost feel like a kid."
