The Independent Expert Panel's 33-page report was published on Friday.
The panel's chair, Rt Hon Sir Stephen Irwin, wrote that MP Coyle had "engaged in foul-mouthed and drunken abuse of a Parliamentary Assistant to another MP" and "used abusive language with racial overtones" to a journalist.
Both incidents took place in a Commons bar.
Sir Stephen was critical of the journalist Henry Dyer, the complainant in the second case, for going public with his allegation before it had been investigated. Mr Coyle was also criticised for giving an interview about the matter while the process was still under way.
Mr Coyle has been suspended from the Parliamentary Labour Party for more than a year whilst the complaints have been investigated.
Whilst the parliamentary process has concluded, the Labour Party has yet to make a decision on his future.
Mr Coyle tweeted on Friday: "I'm deeply sorry for my offensive behaviour and language last year. I have apologised since last February and will continue to do so. I have lived and worked in China, have multiple Chinese family members, and serve a vibrant, diverse community and acknowledge the hurt and upset I caused.
"I'm ashamed that alcohol had become so problematic in my life that I had developed a dependency. After a year-long ban from Labour, I've worked hard to continue battling discrimination, including providing a guide to help in the cost-of-living crisis and successfully campaigning against Transport for London cuts to Southwark bus services and their diverse workforce.
"I'm pleased to have managed a full year without alcohol.
"I'm back, fighting fit having lost three stone. Alcohol no longer negatively affects my judgement, relationships or behaviour. I'm grateful for all the support in stopping drinking, including to friends, family, Labour members, as well as Alcoholics Anonymous (AA).
"I will remain teetotal and I'm hugely grateful to the people in Southwark who have given me so much and been so amazingly supportive. I thank you again for giving me the chance to serve and will not let you down through alcohol again."
Richard Wingfield, chair of the Southwark Liberal Democrats, said: "The Independent Expert Panel’s Report into Mr. Coyle’s behaviour in the Palace of Westminster is clear and explicit and speaks for itself.
"It is clearly right that findings of multiple breaches of Parliament’s Bullying and Harassment Policy, including racism directed towards a journalist, should lead to a period of suspension from parliament.
"All MPs should expect severe consequences for such unacceptable behaviour.
"In the coming weeks it will be for the national and local Labour parties to decide the political future of Mr Coyle as an MP and candidate, and how his past behaviour should be dealt with by the Labour Party.
"In Southwark, only two parties have elected representatives – the Liberal Democrats and Labour. At the next election, Liberal Democrats will be fielding good candidates for every seat, and we will always challenge the record of the Conservatives nationally and Labour across London and in Southwark. We aim to go on winning as many votes and seats as we can. It is clear that our borough needs a Liberal Democrat MP to represent us again as soon as possible."