Hogan, capped twice by the Republic of Ireland, could make his debut for United against Bolton Wanderers this weekend after arriving from Aston Villa.
Wilder first expressed an interest in signing the 26-year-old during the summer transfer window but, after being thwarted then, submitted another approach after learning Villa could finally be prepared to do business earlier this month.
Although Bristol City also enquired about Hogan's availability, Wilder said: "Scott had options but he made it clear that he wanted to join us and that goes a long way in my book.
"I've made no secret of my admiration for Scott and his abilities, we made enquiries about him in the last window and we've had to be patient."
Although Hogan struggled to produce his best form in the Midlands, he is a proven goalscorer at Championship level after netting 21 times in only 27 starts for Brentford before Villa paid £9m to acquire his servives two years ago.
Having started his career with Rochdale, Hogan has also played in non-league for the likes of Halifax Town and Stocksbridge Park Steels.
"He is a player we know a lot about and we are confident that he will be a great addition to what we already have," Wilder, whose side are third in the table, said. "Options at the top end of the pitch are vitally important and in the situation we find ourselves in, Scott offers us a new dimension."