The five clubs have all been named by the former Metropolitan Police commissioner in his final report to the Premier League, released on Friday.
The clubs are set to face a further investigation from the Football Association but it is understood that Newcastle and Bolton are viewed as the most serious miscreants.
Stevens has also expressed concern about 15 agents and third parties involved in some 17 transfers.
Stevens' report specifically lists concerns about two managers.
One is Sam Allardyce, and a conflict of interest with his former agent son Craig and Bolton Wanderers.
The other is Graeme Souness, with Stevens reporting "inconsistencies in evidence" provided by the former Newcastle manager and Kenneth Shepherd, son of Magpies chairman Freddy Shepherd.
Of the 17 transfers, four relate to Newcastle signings (Emre Belozoglu, Jean Alain Boumsong, Amady Faye, Albert Luque), four to Bolton (Ali Al-Habsi, Tal Ben Haim, Blessing Kaku, Julio Correia), three to Chelsea (Didier Drogba, Petr Cech, Michael Essien), three to Portsmouth (Collins Mbesuma, Benjani Mwaruwari, Aliou Cisse) and two to Middlesbrough (Aiyegbeni Yakubu and Fabio Rochemback) while one transfer has not been disclosed.
Lord Stevens said in a statement: "Many lessons have been learned and strict adherence to and enforcement of the recommendations should ensure that the game and the transfer market can proceed in an untainted and transparent manner."
The Premier League will now send the findings to the FA and FIFA.
An FA spokesman said: "Following the final report of the Premier League's Quest Inquiry, the FA will give full consideration to its contents and the documentation that is due to be passed on by the Premier League and Quest.
"The FA has provided full co-operation and support to the Premier League and Quest and will now go through their information as part of our governance and regulation process. This will determine what action is required."
Sports Minister, Richard Caborn, added: "I welcome the transparent approach taken by the Premier League in publishing these findings.
"While it's pleasing to hear that all clubs and officials have co-operated fully with the Stevens inquiry, I am deeply concerned that some agents haven't. They should do so immediately.
"It's now for the FA and FIFA to pursue these agents vigorously and they will have my support every step of the way.
"The role of agents in football will always be controversial and that's why they need proper regulation at national, European and international level."