The defendant, an Austrian identified as Beran A, was arrested on August 7, 2024, the day before the first of three planned concerts by the US pop star in Vienna.
All three dates were then cancelled, to the dismay of fans.
The trial in Wiener Neustadt, near Vienna, will focus on more than that planned attack.
Beran A, who prosecutors say swore allegiance to Islamic State, is also accused, along with Slovak national Arda K, of planning attacks in the Middle East they did not go through with, and of helping a third man who has been arrested on suspicion of carrying out a knife attack in Mecca.
"He is pleading guilty regarding the whole Taylor Swift affair," Beran A's lawyer Anna Mair said before the trial began on Tuesday, adding that he would plead not guilty to the other allegations.
Arda K will plead guilty to travelling to Istanbul with the intention of carrying out a militant attack that he did not go ahead with, his lawyer David Jodlbauer said before the trial.
Both defendants covered their faces as they entered the courtroom, as is common in German-speaking countries to avoid being identifiable in photographs.
Beran A wore a dark blue shirt and jeans, Arda K a light blue shirt and beige trousers.
Prosecutors accuse Beran A of obtaining instructions online on how to make shrapnel bombs of the kind used by Islamic State, producing a small amount of the explosive triacetone peroxide and trying to buy weapons illegally for the planned attack.
He has been charged with various terrorism-related offences as well as belonging to a criminal organisation and making a dangerous threat, and faces 10 to 20 years in prison if convicted.
Prosecutors also allege the two and the third man had planned to carry out one attack each in the Middle East before the Swift concerts, in March 2024: Beran A in Dubai, Arda K in Istanbul and the third man in Mecca.
While each travelled to his designated city, only the third man is believed to have launched an attack - he was arrested on suspicion of stabbing a security official at Mecca's Grand Mosque.
He is still in custody in Saudi Arabia.
Tuesday is the first of four scheduled trial days, with the last on May 21.
