The Northern Premier League leaders have moved to bolster their ranks as they look to continue the early-season momentum which has seen them win 12 of their opening 13 matches in the league.
They sit seven points clear at the top of the division ahead of Saturday's trip to Matlock Town.
Tse arrives at the Boro having featured for fellow NPL side Hyde United already this season, making five appearances in all competitions.
He began his career with Manchester United at the age of 12 before moving to cross-city rivals City, staying with the Premier League champions for six years.
He has spent the majority of his career in Hong Kong and has been capped eight times by his national team since making his debut in 2022.
He adds versatility to the Radcliffe ranks, with an ability to operate as both a centre-back and defensive midfielder.
Joint-manager Anthony Johnson said: "Sean was excellent against us when we played Hyde at home earlier in the season and was someone we actively spoke about after the game.
"We were a bit shocked, but pleasantly surprised when he left Hyde, meaning we could act and bring him into training."
Also making the move to the Neuven Stadium is forward Obasoto, who most recently spent time at Bury.
He began his career in Ireland before joining League Two Morecambe's youth setup.
The 21-year-old lists Macclesfield and Clitheroe amongst his previous clubs but enjoyed most success at Bury AFC, featuring 40 times and bagging 13 goals and 11 assists in their NWCFL Division One North title-winning campaign.
"Abs is someone we’ve been aware about now for a couple of years. His performances for Bury AFC when they were playing at the Neuven were outstanding, which alerted us to his ability," Johnson said.
"We were more than happy to invite him in with us when we heard the news of his departure from Bury, and he has unsurprisingly impressed myself and Bernard enough to offer him a deal."
The pair made their first appearances for the club on Tuesday night, featuring in their 4-3 defeat at home to Chaddertton in the Manchester Premier Cup.