Local paper The Gazette broke the news early on Wednesday evening after the final few points were agreed on the terms of the deal.
Fischer, 21, signs for an initial fee of £3.8million on a three-year contract with the option for a fourth. The fee could then rise with performance-based incentives, as was the case with the fees Boro paid last season for strikers David Nugent and Jordan Rhodes.
Adomah example adds to Fischer's immense promise
The talented young winger, who joins from Dutch giants Ajax, was once a target for some of the world's biggest clubs as he burst onto the scene winning back-to-back Eredivisie titles.
However, a long-term injury to his thigh sustained in February 2014 saw him miss over a year of football, and he found his role in the first team somewhat diminished upon his return to the squad.
Fischer is a right-footed winger who most frequently plies his trade on the left flank, in a manner akin to how Boro fans have seen Albert Adomah play at times in recent years.
Though he has not yet lived up to his incredible potential, Fischer is still a raw talent at 21 years of age and Teessiders will be hoping that the improvement of Adomah under Aitor Karanka will be mirrored as Fischer adapts to life in England.
Fischer adds natural left-flank balance
The arrival of Fischer adds balance to Middlesbrough's side with fellow left-wingers Stewart Downing preferring to play through the centre and Carlos de Pena struggling to make any impact since joining the club last summer.
It is also a positive start to a summer which is likely to see additions made throughout the squad as chairman Steve Gibson looks to help his side be competitive in their first top-flight season since relegation in 2009.