The watchdog has revised its initial idea for a five-year tender amid worries over the cost and disruption that could cause.
Other recommendations in the report include the Financial Reporting Council's (FRC) audit quality review team to look at every FTSE-350 audit every five years and a shareholder vote at annual general meetings on whether audit committee reports are satisfactory.
There is also to be an end to clauses in loan agreements specifying a company auditor must come from one of the Big Four accountancy firms, KPMG, Ernst & Young (EY), PwC or Deloitte
Other proposals such as mandatory rotation, joint audits and further restrictions on the provision of non-audit services have been dropped.
Laura Carstensen, chairman of the Audit Market Investigation Group, said: "Instead of long, unchallenged tenures which can reduce the appearance of objectivity and scepticism essential to an effective audit, there will now be far greater transparency and scrutiny.
"It will also open the door to other auditors who now have the chance to compete regularly for business and show they're up to the mark."
The FRC had wanted more time for its year-old rule requiring companies to consider re-tendering at least once every decade to gain acceptance but the publication of the CC's findings was hailed by mid-tier accountancy firms as providing them with an opportunity to compete with the Big Four.
Scott Barnes, chief executive of Grant Thornton, said: "We are pleased to see the CC taking robust action to address the identified fundamental flaws in the audit market.
"The CC's remedies have the potential to produce positive change in the market to encourage continued improvement in audit quality and, in turn, the actions have provided a clear connection between auditor, audit committee and shareholder to drive greater innovation and competition in the market."
However, there was recognition that real change in the market will take a number of years.
James Roberts, senior audit partner at BDO, said: "While some may regard the outcome of the investigation as being less radical than many would have hoped, the real importance of the investigation has been to shine a spotlight on a previously dark recess of corporate governance. That's the real victory here.
"We are under no illusion that, despite the investigation, the establishment of real and sufficient competition is a long-term undertaking."
James Barbour, director of technical policy at the Institute of Chartered Accountants of Scotland, said the industry was pleased the CC had taken on board many recommendations, particularly with regard to tenders.
He said: "Whilst mandatory retendering is not, in our view, the optimum solution, we do welcome the fact that the CC has extended the maximum possible period between tenders to 10 years from the five featured in its provisional decision.
"This does increase the level of flexibility available to companies, however, we would have preferred companies having the option to extend this period by up to two years to allow for unforeseen circumstances."
The Big Four firms had a mixed reaction to the outcome.
James Chalmers, head of assurance at PwC, said: "This is a sensible outcome.
"Taken together, these measures will enhance competition, transparency and quality."
But Hywel Ball, managing partner for assurance at EY, suggested the CC had failed to provide evidence the current system leads to a lack of competition.
European Union regulators are also looking at the audit market, partly because auditors gave banks a clean bill of health in the run up to and during the financial crisis, which could yet see the length of time between tenders changed again.
David Barnes, managing partner at Deloitte UK, said there will be some uncertainty until the position in Europe is finalised.