Sefton Council is now launching a consultation with library users into the proposals which will run from October 29 through to January 14.
Bill Esterson said that while it is good news Labour Councillors have chosen the option to save Formby Library, it is still crucial that people take part in the consultation.
Bill said: "The Tory-Lib Dem Government has cut Sefton Council's budget by £64.5m over the past two years, rising to £107.5m over the next two.
"That's one of the greatest cuts to a local authority anywhere in the country.
"We all know how vital our local libraries are in our communities, particularly to many of the most vulnerable people. We know here in Formby that the library is one of the busiest in the borough.
"So it is great news that Formby Library has been earmarked to be saved, but it is absolutely vital that people in Formby still take part in the consultation process. We need the views of the people of Formby heard."
Bill said Sefton's Labour Councillors were working hard to negate the effects of the Tory-Lib Dem cuts.
Bill said: "Sefton Councillors are in an impossible position as they try to balance the inadequate budget they have been given which must pay for vital services in the borough.
"But libraries are a vital part of the community. It is a place where people of all ages can go and get access to information, the internet and books, and also meet other people.
"For many older people the library is the only way they get to meet people. Formby Library is an integral part of the community of Formby. That's why I am delighted it has been saved."