Pulis, 55, has been out of work since he left Stoke City in May and was officially unveiled at the club's Beckenham training base on Monday.
Palace's 1-0 win at Hull City on Saturday saw them climb off the bottom of the Premier League table, but they are still three points from safety.
When asked why he took the job, Pulis - who has never been relegated as a manager - said: "Why not? It's a club in the Premiership. It's a smashing club.
"It's got great history. It's going to be a tough job, I know it is going to be a tough job.
"It's an opportunity and a chance to achieve something Palace haven't achieved, which is to get promotion to the Premier League and stay.
"We will be underdogs, everybody expects us to get relegated and it is nice to prove people wrong.
"I'm still very ambitious. I like climbing hills. This is going to be a tough job but one that I'll relish."
"It was important that it was right. We ended up having three meetings together," Pulis added.
"We discussed different things. Steve said it was right that he wanted to speak to other people and get a full overview. It was right for Palace that they wanted to make sure they get the right man.
"I've been promoted out of every division in English football, I've made it to an FA Cup final and the last 30 (last 32 of the 2011-12 UEFA Europa League) in Europe.
"It annoys me in this country that you do get pigeonholed in certain things. Everybody talks about not being relegated. As a manager, I've got a few promotions and I've been pretty successful given the chance."
"We've got six games before Christmas, until the window opens again," he continued.
"There's an opportunity to wheel and deal in the window. Watching them on Saturday, I thought the attitude of the lads was absolutely terrific.
"(Former caretaker manager) Keith (Millen) has made it clear to me that it's a really good group of lads and they've got great spirit. We will most probably need to wheel and deal a little bit in the window but I know that Steve will trust me."
