Meja came up through the ranks of Green Commandos SC of the National Super League. With Lihrembe Arsenal FC he won the 2018 and 2019 Cleophas Malala Super Cup, winning the Golden Boot Award in both editions of the tournament.[1] In January 2020 he signed a three-year contract with Tusker F.C. of the Kenya Premier League. He spurned interest from AFC Leopards and Kakamega Homeboyz for the promise of top-flight minutes and so that he could play with his brother Sammy.[2] He scored his first goal for the club on 13 December 2020 against Gor Mahia. He came off the bench to score the game-winning goal of the 2–1 victory.[3] He was named the Premier League and Tusker's Player of the Month for January 2021 after tallying four goals and an assist for the month.[4][5] In March 2021 it was reported by local media that Meja's progress was being tracked by Zamalek of the Egyptian Premier League and Tanzanian club Simba.[6]
In September 2021 Swedishtop-tier club AIK communicated that they had signed Meja on a five-year deal and that he would join the club for the pre-season in January 2022.[7] Meja’s official arrival at AIK was announced in January 2022 at the opening of the transfer window.[8] The player's contract was set to run through 1 September 2026.[9]
In January 2023 Melo was loaned out to Norrby IF for the 2023 season.[9]
In March 2024, Meja joined AFC Eskilstuna on loan for the 2024 season.[10]
^"AFC lånar Henry Atola Meja från AIK" [AFC loan Henry Atola Meja from AIK]. www.afc-eskilstuna.se (in Swedish). 18 March 2024. Retrieved 19 March 2024.