Financial terms of the deal have not been disclosed.
Founded in 1987, TSP Projects is a subsidiary of British Steel, which was placed into compulsory liquidation in May.
The acquisition of TSP Projects by Systra is expected to save more than 400 jobs.
The deal is part of the French firm’s strategy to position its British arm as a major player in the local mass transit, mobility and complex infrastructures markets.
Systra CEO Pascal Mercier said: “This acquisition is a game-changer for our UK and Ireland business, placing us among the leading UK consulting engineering firms.
“This is a good fit between two like-minded companies with a shared commitment to excellence, safety and innovation.”
TSP Projects CEO Craig Scott said: “This is a great opportunity for TSP Projects staff, clients and partners. Systra is a like-minded organisation with similar values and a focus on technical excellence.
“Systra ownership will bring with it all the benefits of a global engineering business, including access to high calibre technical expertise to complement and enhance TSP Projects.”
In June, Systra secured a contract to design rail systems, workshops and rolling stock for Line 7 of the Santiago Metro in Chile. The contract was awarded by Metro SA.
Furthermore, Systra, in a joint venture (JV) with Talgo, secured a $138.9m rail car overhauling contract in the US last month.
Awarded by the Southern California Regional Rail Authority (SCRRA), the contract will include rebuilding up to 121 passenger rail cars.