Trier was not selected during the 2018 NBA draft on Thursday.
The 22-year-old Seattle native played three seasons for the Wildcats, and he is coming off a highly productive 2017-18 campaign.
Last season, Trier averaged 18.1 points, 3.2 assists and 3.0 rebounds per game, while shooting 50.0 percent from the field and 38.0 percent from three-point range.
He was named First-Team All-Pac-12 last season and was the Pac-12 tournament's Most Outstanding Player in 2017.
Trier was suspended for the first 19 games of the 2016-17 after testing positive for a performance-enhancing drug. He was also suspended briefly last season, but it was determined that the trace amount of banned substance in his body stemmed from the previous year.
New York presents a good situation for Trier since the Knicks don't have a ton of depth or quality at shooting guard or small forward.
Tim Hardaway Jr. is their best option at those spots, with rookie first-round pick Kevin Knox, veteran Courtney Lee and Ron Baker providing the primary depth. If Trier impresses leading up to the 2018-19 regular season, he could conceivably make the team and work his way into the rotation as a rookie.
If Trier doesn't make the team, the two-way contract will allow the Knicks to retain his rights while he plays in the G League.