Bishop Mehaffey, who was 88, died on Monday evening surrounded by his family.
Dr Mehaffey led the Diocese of Derry and Raphoe for more than 20 years, from his consecration in September 1980 until his retirement in January 2002.
During his time as bishop, he officiated at funerals of many parishioners killed in the Troubles.
Mr Eastwood said that Bishop Mehaffey’s ministry and close friendship with Bishop Edward Daly was a symbol of the power of partnership and reconciliation.
He said: “I was deeply saddened to learn of the death of Bishop Mehaffey on Monday evening.
“His ministry was a constant source of hope during the darkest days of conflict and under the immense burden that violence brought to our city.
“The defining friendship between Bishop Mehaffey and Bishop Daly, two people from different traditions who saw the best in each other and in our communities, was an enduring symbol of the power of partnership and reconciliation to shape lasting change.
“They lived the Christian values that they preached every day – generosity, compassion and an inextinguishable love for this city and everyone who lives here.
“I know they were incredibly proud, and deeply humbled, to receive the freedom of Derry together in 2015.
“His work as a founding member of the Inner City Trust will leave a lasting legacy on this city and helped, in the midst of immense destruction, to heal the scars of conflict.
“My thoughts are with his wife Thelma, their children Wendy and Tim and their whole family and wide circle of friends at this difficult time.
“I hope they are comforted by the pride that this city takes in James’ memory,” added the Foyle MP.
The Catholic Bishop of Derry, Dr Donal McKeown, also paid tribute.
He said Dr Mehaffey’s “very significant personal friendship and partnership with Bishop Edward Daly… gave witness to a powerful message of harmony and peace building”.
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