Councillor Patrick Harley, leader of Dudley Council, said: “We are tremendously proud of our borough and we have huge ambitions for our future."
Lord Austin, former Dudley North MP, hailed the news and said: "Dudley lit the spark that fired the industrial revolution, changing not just the Black Country or even Britain, but the whole of the world, and with the best college in the country, the genuinely world class tourist attraction at the Black Country Museum and the brilliant new university campus we are building, this could really help put the greatest place in Britain on the map."
Andy Street, the Mayor of the West Midlands, said he will support the borough's application.
He said: “It is brilliant news that on Black Country Day Dudley Council have announced their intention to become a city, and I want to lend them my full support.
“Dudley might not have a cathedral, but it has a wonderful castle and a history to be incredibly proud of as the home of the industrial revolution. It also has so many assets to support its bid for city status, such as a population bigger than cities like Newcastle, a genuinely world-leading museum, and of course a vibrant economic future thanks to the investments currently being made.
“I wish the council all the best and I hope to see Dudley become the West Midlands’ fourth city.”
Speaking after the announcement, Marco Longhi MP for Dudley North, said it further places Dudley on the map.
He said: "This is very good news. City status conveys a status and reputation that recognises the past, present and aspirations for where we want to take Dudley.
"It further places Dudley and its people on the map and it complements the massive investment the Government is making with its infrastructure redevelopments.
"As we role out our regeneration plans this will attract even more external investment as Dudley continues to climb up the league table. This will mean more jobs and an improving quality of life for all.
"Today is Black Country Day and as Dudley is its capital I cannot think of a more fitting recognition.
"I do hope we will be successful, and I will be wholeheartedly supporting the application as we come together to mark HM the Queen's Platinum Jubilee."
Dudley's top attractions such as the canal and tunnel trust, Black Country Living Museum and Dudley Zoo welcomed the news.
A spokesman for Dudley Canal and Tunnel Trust said: "Here at Dudley Canal and Tunnel Trust we think it amazing news and we will be doing everything we can to support the bid.
"Dudley is a very exciting place to be at the moment with all the investment and developments. It’s great to be located in an area which is so forward looking and wanting to bring in new businesses, visitor offers and improvements.
"Attracting more visitors to the area and encouraging those who live and work here to get out and enjoy what is located all around them can only help us all to thrive."
And Andrew Lovett, director of the Black Country Living Museum, said: "For many people in Dudley Borough the town is viewed as the historic capital of the Black Country, so it will be encouraging to see how public support for a city bid develops and what it can do to enhance the standing and awareness of the Black Country more widely.”
Zoo director Derek Grove said: "Similar to its Zoo and Castle, Dudley is in the process of change and is working hard to make the most of the opportunities the 21st century can deliver, while celebrating and not losing touch of its unique heritage.
"Having been born, lived and worked in the borough all my life, like so many locals, I’ve experienced the regeneration and transformation in Dudley first hand.
"Dudley has so much to offer for a great day out, with the leisure attractions at the base of Castle Hill already welcoming over 800,000 people annually, not to mention the multitude of green spaces which help make the area such an attractive place to live, work and relax.
"The city status bid is the ideal opportunity to showcase to the nation what we here in Dudley can deliver and can offer in the future. It’s an exciting time for the borough."