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Henderson's contract was ended a year early after Ajax missed out on the league title on the final day of last season.
The decision was reportedly driven in part by the club's financial difficulties, with Henderson their biggest earner.
The 35-year-old was involved in controversy during his 18 months at the club.
On 30 January, Henderson played in a 2-1 Europa League win against Galatasaray but refused to captain the side or join his team-mates in their goal celebrations.
Then-manager Francesco Farioli subsequently declined to comment on speculation linking Henderson with a move to Monaco.
A few days later, following a win against Feyenoord, Henderson got into a heated exchange with Dutch football journalist Mike Verweij, who questioned whether the former Liverpool captain had agitated for the move, which he denied.
Following the public row, Henderson only started a further nine games.
During his time at Ajax, he started 30 league matches, completing 90 minutes on 20 occasions.
Henderson will effectively fill the void left by Christian Norgaard at Brentford and he has big shoes to fill.
Since his Premier League debut in 2021, the Denmark midfielder has made an unrivalled 201 interceptions, while he also ranks second overall for recoveries (844) and third for tackles won (189).
Henderson has perhaps not played as many full games as he would have liked since ending his controversial stint in Saudi Arabia to join Ajax in January 2024 but he has still been effective in Amsterdam, albeit in a less well-regarded league.
He created the joint-highest number of chances of any Ajax player in the Eredivisie last season.
He also completed the most passes and crosses, and made the most tackles and interceptions combined, of any Ajax midfielder.