Mr Hume, who was a key architect of the peace process and won a Nobel peace prize for his efforts along with former UUP leader David Trimble, died last month. He was aged 83.
The Servant and Change were written by musicians as part of the Making the Future programme at Derry’s Nerve Centre.
The songs received their first public airing at the arts centre on Thursday afternoon.
Creative media trainer at the centre Jude Mullan said the songs were two of three composed by around 15 people taking part in the programme.
“They’re really lovely with just singer and acoustic music; they’re very thought-provoking,” he said.
Mr Mullan said the programme, which was run virtually, involved established musicians and songwriters working with three groups to create the songs with accompanying remote workshops by artists such as Undertones guitarist and songwriter, John O’Neill.
The programme was run as part of PEACE IV, European funding, by the Nerve Centre along with National Museums NI and examined the art of song writing.
Each group was mentored by songwriters, Paddy Nash, Glen Rossborough and Danny Larkin.
The Servant and Change were composed by the groups mentored by Mr Nash and Mr Larkin.
The new songs – along with another performance dedicated to life in lockdown – are available through the Making the Future website at www.makingthefuture.eu
“When they were settling on subjects for the songs it was just around the time that John passed away and two of the groups felt it would be a suitable subject.
“John was very much in the air and they related to that.”
Mr Mullan said the songs were particularly appropriate because of the huge support Mr Hume gave the Nerve Centre.
“We are delighted to host such a fantastic event given the connection with John who, not only spoke at the opening of the Nerve Centre, but along with his wife Pat were supporters of our organisation over the years,” he said.