Castle mentioned during the AEGON Championships that Lloyd's alleged personal issues would place him out of the running of being appointed the new chief executive of the Lawn Tennis Association.
The statement, quoted by The Guardian, said: "Mr Castle later accepted that his comments were without foundation and apologised to Mr Lloyd for any embarrassment or distress caused. The parties have now agreed terms to bring the matter to a close, which involves the payment of damages and legal costs.
"However, Mr Castle would like to put the record straight and express again his personal apology to Mr Lloyd. He made his remarks, which were completely without substance, in the hurried exchanges of a live debate.
"Mr Lloyd has accepted Mr Castle's apology and the payment of damages. Mr Lloyd and Mr Castle are pleased to have been able to resolve matters amicably and now consider the matter to be behind them."
Castle made the comments live on BBC2 during a rain delay at Queen's.