A Leeds City Council media briefing this evening confirmed the move, with £59m available for the region to support the measures.
It comes after Hull and the East Riding was announced as the latest places to move in Tier 2 earlier in the day.
South Yorkshire was placed under the highest Tier 3 restrictions on October 24.
While the chief executive of North Yorkshire County Council has said its Tier 1 status is hanging “by a thread”.
A joint statement from the leaders in West Yorkshire said the move was taken “with great reluctance”.
It said: “The virus spread is now at a critical juncture. Not only are infections rising in our region, particularly amongst the elderly, but we already have evidence that the NHS is starting to struggle to deliver essential elective care.
“Once it became clear that heightened restrictions would be necessary, we have been negotiating hard to secure a package of support for our region and our residents - with the aim of reducing the financial uncertainty for people and businesses.
“For now, to enable us to take the advised measures to protect people’s health and wellbeing, we have secured a package worth an additional £59.3m to begin to help support West Yorkshire through this time.”
They added: “That aside, we remain deeply concerned that the impact on the people of the region and the West Yorkshire economy has been desperately underestimated by Government.
“Leaders have been promised further conversations with Government ministers in the next few days to discuss local schemes to build on and continue to support the economic recovery of the region.”
Leader of Calderdale Council, Tim Swift, added: “As the weather changes, so do people’s habits, but unfortunately the change in seasons have had a dramatic effect on the number of Covid cases in Calderdale - our rate is currently 20 times that seen at the end of August.”
He added: “We know that moving into Tier 3 is an unwelcome step in what has been an unrelenting period of upset, but it’s important to remember that the sooner we bring the virus under control, the sooner we can move out of restrictions.
“The fact of the matter is that the virus is too easily spread in groups of people and it’s extremely important that we limit contact with others to bring the infection rate under control in the borough and the wider West Yorkshire area.”
While Bradford leader Susan Hinchcliffe said: "Let’s be clear, further economic restrictions on Bradford and West Yorkshire are going to be damaging for businesses and jobs. There is a “template” of funding available from Government to support these businesses but I do not think it will be enough. Neither were Government in the mood to give us more. Government are seriously underestimating the economic impact of these measures and we in West Yorkshire will challenge them to improve upon them.
“No one can deny that the infection rates are now very high indeed so action needs to be taken. The Government has a tiered approach to how to manage the infection and for areas with high infections this is the next step in their programme. They have told us they are not contemplating a national lockdown as we saw at the start of the pandemic. So this is the only intervention on offer."