The 38-year-old former Red Bull Salzburg and Al-Ahli boss told the club's website: "It is an incredible honour to become head coach of Newcastle United.
"This is one of the biggest clubs in European football, with a unique history, identity and supporter base, and I am excited to experience that passion and connection first-hand.
"When Newcastle United comes your way, you take notice. The ambition of the club, the vision for the future and the opportunity ahead made this an incredibly compelling place to be.
"I have followed the club's journey closely in recent years and the progress that has been made is clear for everyone to see.
"I am incredibly excited about the future. I fully and unreservedly believe in this project, the ambition and the direction the club is taking. There is a clear vision, strong leadership and an exceptional platform to build on.
"I cannot wait to get started and will attack this opportunity. I give my complete commitment and total energy to bringing further success to Newcastle United."
Jaissle was forced to end his playing career due to injury at the age of 25.
His first managerial job came with Austrian side Liefering, whom he led to a second-placed finish in the second tier, the club's joint best-ever position.
Jaissle took charge at Red Bull Salzburg in 2021, winning successive Austrian titles as well as the Austrian Cup.
He then joined Al-Ahli in 2023 and led them to AFC Champions League titles in 2025 and 2026.
The German has big shoes to fill, with Howe revitalising a club that had struggled for decades in his five years at the helm.
He replaced Steve Bruce in November 2021 and won the League Cup in March 2025 - beating Liverpool in the final to clinch the northeast side's first major trophy since 1969.
The former Bournemouth boss also led Newcastle to Champions League qualification in 2023 and 2025.
But hampered by star striker Alexander Isak's protracted move to Liverpool, Howe came under pressure as the Magpies finished 12th in the Premier League last season, with 17 defeats in their 38 games.
Newcastle reached the Champions League last 16 but were hammered 8-3 on aggregate by Barcelona.
The club have since been depleted by the close-season departures of Italy midfielder Sandro Tonali to Tottenham and England forward Anthony Gordon to Barcelona.