The German midfielder was released by Wolfsburg at the end of last season after a campaign wrecked by a knee injury and was without a club until Toffees boss David Moyes offered him a short-term deal in November.
Hitzlsperger, who previously played in the Barclays Premier League for Aston Villa and West Ham, has impressed in his seven appearances for Everton and has now signed an extended deal until the end of the season.
The 30-year-old told evertontv: "When I was out in the summer I thought maybe I'd played my last game already. Now I'm back at a very, very good level in the Premier League, playing for a huge club and it's so enjoyable.
"I'm over it now and I don't want to look back really. It happens and I think most players go through it. It came unexpectedly to be honest but when it did come it was something I knew I had to deal with.
"I tried to be positive and I was most of the time. Fortunately that period is over now, it's behind me and I'm just looking forward to the next few weeks and months.
"I think now I'm fully fit, there's not any problems and I think it's gone well. I spoke to the manager a few weeks ago and he told me he's pleased with my efforts."
Hitzlsperger is now hoping he can help Everton qualify for the Champions League, and he believes the Toffees, who currently sit fifth, are in with a great chance.
He said: "There's so many good footballers in this team and the work ethic is tremendous, so I think we're well equipped.
"But this league is quite tough because you have the usual three or four teams up there that have the financial power and make it very, very difficult.
"It would be a tremendous achievement if we get into the top four. I think we have it in us, we've proved that this season. It's only four months but it will be a long season for us and we've just got to maintain that level of performance we've shown."