Weghorst has won 39 caps for the Netherlands, scoring 12 goals, notably a winner in the 83rd minute of their opening Euro 2024 match against Poland.
Oranje coach Ronald Koeman has used Weghorst as a "super sub", the striker famously hitting a dramatic 101st-minute equaliser in stoppage time against Argentina in the World Cup quarter-final.
Ajax technical director Alex Kroes said the 32-year-old Weghorst would provide an "absolute top sporting experience."
"He is a high-scoring striker who is always making things difficult for every opponent," added Kroes, whose Ajax team is hoping to bounce back from a horror season last year.
Weghorst, who said he supported Ajax as a young boy as his grandfather was a huge fan, said he had come to Amsterdam determined to fight for a first-team place.
"It's up to me to convince the coach and everyone else that I can be the striker at Ajax. That's the goal," he said in an interview posted on the club's website.
Weghorst has played for several clubs around Europe, starting his career at Dutch league sides FC Emmen, Heracles Almelo, and AZ Alkmaar.
He went to Wolfsburg to play in the German Bundesliga before joining Burnley.
During his time in northern England, he went out on loan to Besiktas in Turkey, and Manchester United, where he played 17 Premier League games without finding the back of the net.
Another loan spell saw him back in the Bundesliga with Hoffenheim before Burnley sold him to Ajax for an undisclosed fee.
Ajax endured one of the worst seasons in their history last year, at one point propping up the Eredivisie table and suffering humiliating losses to rivals Feyenoord and PSV Eindhoven.
After an encouraging 1-0 win over Heerenveen on the opening day this year, it became clear that the corner had not yet been turned as they lost 2-1 away to NAC Breda.
