Su became premier in 2006 replacing Frank Hsieh, the man who defeated him in last week's primary for the Democratic Progressive party (DPP).
He is the fifth premier to resign in the seven-year tenure of president Chen.
The premier heads the cabinet and is responsible for winning legislative support for government policies.
"This will be [Chen's] last year in office and he may want to make changes to cope with the new situation," Su said earlier on Saturday. I'm willing to co-operate, and have reported this to him."
"Although I have given up my duties, I have not given up on Taiwan," Su said.
The contest for the party's presidential nomination had provoked bickering among the two front-runners.
On the eve of the vote, Hsieh's camp attacked Su for planting a story in a magazine accusing the former premier of corruption. Su then challenged Hsieh to prove his innocence.
Hsieh and two other candidates, Annette Lu, the vice president and another ex-premier, Yu Shyi-kun, also accused Su of using his position as head of the cabinet to lobby votes by promising favours to local politicians.
Su is popular among grassroots supporters after having been magistrate of the important Taipei county in the north and Pingtung county in the south.
He has also served as secretary-general of the presidential office under Chen and chairman of the DPP, a post he resigned from in December to take responsibility for a poor showing in elections.
In Taiwan's political system, the democratically elected president appoints the premier, who forms the cabinet and runs day-to-day government.