Talented Sweden striker Wangerheim is the latest addition to a United attack that has also been reinforced with Germany star Lea Schuller this window.
Wangerheim arrives in Manchester after scoring 17 goals for Hammarby to help them finish second in the Swedish league in November.
She was an unused substitute for Sweden when England beat them on penalties in the European Championship quarter-finals last summer.
Skinner said the new signing will allow his side to be “more unpredictable” in their quest to win titles this season.
“I thought we were becoming too predictable,” he said. “The Manchester United spirit is about attacking with speed and invasion – and she brings that in abundance.
“She is a lovely quiet character off the field. On it, she gets alive. She wants to take people on and run behind and I felt we had lost that a little bit.
“She is 21 but has so much experience already. She had 3,000 minutes in 2025 but still sits in the category of us being able to add lots of quality to her football too.
“She is a rare find.”