Osula played 21 times for the Blades in the English top flight as they were relegated last season, having spent the previous campaign on loan in the third tier at Derby.
He started his career with his hometown club Copenhagen before moving to Yorkshire side Sheffield United in 2018.
"It's a big club, a great club, so I'm very happy for the opportunity to join Newcastle United," he told his new team's website.
"It's a great opportunity, and as soon as I heard about Newcastle's interest I knew I had to take the chance to join this club if it came.
"It has come and I'm really happy to be here."
Magpies manager Eddie Howe added: "William is a talented young forward with all the attributes to be an exciting player for Newcastle United.
"We have watched his development closely and we are delighted to have the opportunity to work with him in this next step in his career."
Newcastle, who finished seventh in the Premier League last season, begin the 2024/25 campaign at home to Southampton on August 17th.