Governor Deval Patrick on Thursday will propose eliminating the state’s troubled patchwork of 240 public housing authorities and replacing them with six regional agencies in an effort to eliminate waste and corruption from the housing program for low-income and elderly people, state officials say. Public housing, which shelters more than 300,000 people in Massachusetts, has been buffeted by controversy for more than a year since the Globe reported the inflated $360,000 salary of Chelsea’s housing director. Several other directors were forced to resign amid allegations of abuse of their position. Patrick’s proposal, which is sure to be controversial on Beacon Hill, would consolidate public housing management — including budgeting, planning, and administrative functions — into six central offices, while leaving a corps of managers and maintenance workers at local housing authorities. Local boards would be cut, eliminating the need for more than 1,000 politically appointed commissioners.