CSSF said the Swiss bank had provided "proof and guarantees" regarding changes at the Luxembourg-based host of the Luxalpha fund.
The watchdog had criticized UBS for custodial failures after Luxalpha was found to have funnelled investors' cash to Mr Madoff's investment firm.
However, it said it was now satisfied that the "necessary infrastructure and necessary internal rules" had been put in place to protect clients.
According to Reuters, investors in Luxembourg lost around $1.7 billion to the Madoff scam, most of which was linked to Luxalpha.
Speaking to Bloomberg, lawyer Pierre Reuter of Thewes & Reuter, which is currently handling around 70 claims against banks, fund and auditors hit by the Madoff affair, said: "It's extremely frustrating for investors to see that the bank was faulted for a grave breach and now, three months later, everything seems to be in order."
The decisions of CSSF and UBS "lacked complete transparency", he added.
Mr Madoff faces up to 150 years in prison after pleading guilty to orchestrating a $65 billion fraud.