Cases involving 21 people - among them actors Nigel Havers and Rhys Ifans, and actress Kym Marsh - were settled at London's High Court.
The settlements all involve undisclosed damages, costs and an apology.
Further phone-hacking claims against MGN are due to be heard in court next year if agreements are not reached.
MGN publishes the Daily Mirror, the Sunday Mirror and the People.
David Sherborne, representing Mr Havers, whose acting credits include Chariots of Fire and Coronation Street, said his client had been targeted by phone hacking between 2000 and 2004.
The actor had been subjected to intense intrusion when he was nursing his late wife through the final stages of cancer, Mr Sherborne said.
Mr Ifans, best known for his role in the film Notting Hill, lost a number of close friends as a result of the distrust created by newspaper stories published as a result of hacking, the hearing heard.
Ms McCall's case involved a March 2007 article named Davina's Stalker Terror, which MGN admitted had been published after her voicemails had been intercepted.
Other settlements involved businesswoman and socialite Caroline Stanbury, PR consultant Alison Griffin, publicist Clair Dobbs, and film-maker Jim Threapleton - the ex-husband of actress Kate Winslet.
The list also included actress and Loose Women panellist Lisa Maxwell, actress and singer Suzanne Shaw, actresses Caroline Chikezie, Tina Hobley, Holly Davidson, Kate Ford, Samia Ghadie and Lucy-Jo Hudson and actors Ben Freeman, Alan Halsall, Christopher Parker and George Calil.
Christopher Wenn, from Charles Russell Speechly, which represented a number of the claimants, said he was "delighted" MGN had also apologised for the hacking, as well as paying damages.
Last year, damages totalling nearly £1.25m were awarded to eight people whose phones had been hacked by Mirror Group journalists writing celebrity stories.
Actress Sadie Frost was awarded £260,000 and ex-footballer Paul Gascoigne £188,250, while Soap stars Shane Richie, Shobna Gulati and Lucy Benjamin also received payouts.
Following the verdict, MGN announced it had set aside an extra £16m to deal with further claims - in addition to the £12m provided in 2014.
Celebrities including TV presenter Davina McCall have been paid damages after settling phone-hacking claims with Mirror Group Newspapers (MGN).