Nuhiu finished the 2017-18 season as the club’s top goalscorer with 14 goals following a renaissance in the second half of the campaign, with nine goals arriving during a purple patch between March 17 and the end of the season.
The Kosovo international, who has now spent five years with the Owls, says he is delighted to have extended his stay.
The 28-year-old said: “Sheffield Wednesday was the club to open the door for me to come to England and my priority was to stay here.
“The manager and the club has shown that they want me to stay, so there was no doubt that we could find an agreement and I am very pleased with that.”
Former York City defender Graham Potter is among the candidates Swansea City are expected to approach to replace Carlos Carvalhal, with the ex-Owls head coach to leave the Swans at the end of the season.
Potter, 42, is currently in charge of Swedish club FK Ostersunds, who has guided them from the fourth tier of Swedish football to the top flight, while former Wales boss Chris Coleman is also thought to be in the frame.
This season Potter has led Ostersunds to the last 32 of the Europa League, beating Galatasaray, Hertha Berlin, drawing with Atletico Madrid and giving Arsenal a scare by winning at the Emirates before eventually going out on aggregate.
He has previously been considered by Swansea, whose relegation is set to be confirmed after Sunday’s game with Stoke.
Yorkshire-based goalkeepers Keiren Westwood, Darren Randolph, Colin Doyle and Ian Lawlor are among the call-ups into Martin O’Neill’s provisional Republic of Ireland squad ahead of their upcoming international friendly matches with France in Paris on May 28 and at home to the USA at Dublin’s Aviva Stadium on June 2.
Sheffield United defender Enda Stevens, Leeds United midfielder Eunan O’Kane and outgoing Hull City player David Meyler will also join up with the senior Irish squad ahead of a ‘warm-up’ game with Celtic on May 20.
Ireland will face the Scottish Premier League champions in a testimonial game for the Bhoys’ captain Scott Brown.
O’Neill will make his final squad decision shortly after the game with Celtic.