He made the apology to the House of Commons having been told to do so after he repeatedly failed to register payments from his newspaper column and books within the set time limit.
"The committee concluded that Mr Johnson breached the rules of the House by failing to register remuneration within the required timetable on nine occasions", the committee said in a report.
MPs are required to declare payments for any work carried out in addition to their duties as an MP, in the Register of Members' Interests.
"In considering the appropriate sanction, it took into account what it considered to be aggravating and mitigating factors, and recommended that Mr Johnson make an apology to the House on a point of order".
The letter added that this was not Johnson's first discretion, "by no means the first time within the past year or so that there has been a failure on his part to comply with the rules".
MPs have to register any changes to their financial interests each month but Mr Johnson was late four times involving nine payments, the parliamentary watchdog found.
Since quitting as foreign secretary he has resumed writing a column for the Daily Telegraph - for which he earns nearly £23,000 a month.
The late declarations included a series of rights and royalty payments from Bulgaria, Hungary, the Czech Republic, France and the U.S. for books "already written" by Mr Johnson.
She said: "However, these payments can not have been entirely unexpected and, given that the house has made explicit that it expects members to fulfil their responsibilities conscientiously, it would have been prudent for Mr Johnson to have had an administrative system in place to ensure his compliance with those rules".
Johnson had now assured her he had a system in place to prevent this happening again, Stone added.
The nine late registrations had a total value of £52,722.80, and were largely royalties or for the sale of rights on books already written, Ms Stone said.
Kathryn Stone, parliamentary commissioner for Standards, said the number of late registrations suggested a "lack of attention to the House's requirements, rather than inadvertent error". She added: "Neither of those criteria are met in this instance".