The historic, grade II listed bridge has been closed since December, when the force of the Boxing Day floods washed out its foundations and undermined the road above.
It left a gaping hole over the Calder and Hebble Navigation Canal, but a new arch was today lifted into place to make the new bridge stronger and more resilient.
Work on the bridge, which will look similar to the old one, is expected to be complete by the end of the year.
The Government has pledged up to £5m for the replacement of the damaged bridge. As part of the package the Canal and River Trust is also providing its expertise to replace the nearby Crowther Bridge, Brighouse, which is owned by Calderdale Council and was also severely damaged by the floodwaters.
A temporary footbridge next to Elland Bridge which was constructed in January will remain in place throughout the works.
Calderdale Council leader Tim Swift said: “This is a really important step forward in showing the progress that is being made in reopening the bridge.
“This was the most iconic piece of damage caused by the floods so I think it’s really important for the whole community to see that it is making good progress. It’s really a sign that Calderdale is getting back on its feet after the floods.”
The bridge is expected to fully re-open to traffic at the end of the year, with all repairs completed by early 2017.
Coun Swift said: “It’s on track, it’s a very complicated project and it’s great to see this happening.
“I know how much disruption the closure of this bridge has caused for everybody.
“I think people have been really understanding of the problems it has caused and appreciate work is going on to get it sorted.
“It will be fantastic to see it finished, it will be great for local businesses, great for the community and the wider community as it had an affect on traffic almost everywhere this end of Calderdale.”
Graham Ramsden, senior project manager for the Canal and River Trust, added: “This is a pretty significant day in the life of getting the bridge restored
“We’re lifting in the concrete arches today and all this week. The first two went in on Monday, the next two are coming in today and by the end of the week, all will be in position.
“The next part will be when our specialist stonemasons come in and start to put back the original stone from the bridge into the walls.
“This is the biggest individual project the Canal and River Trust is doing in the country right now.
“The floods of Boxing Day were pretty significant events in the Calder Valley and its important we get this bridge back up and running as soon as possible.”
He added that the new bridge would have a concret core to make it significantly stronger and resilient in the face of any future flooding.