Lyra McKee, 29, was shot by suspected dissident republican gunmen during serious rioting in Creggan on Thursday night.
She was rushed by police landrover to Altnagelvin Hospital but tragically died of her injuries.
Police chiefs blamed dissident republican terrorists for murdering Ms McKee.
Mr Eastwood said Ms McKee’s murder was a “grotesque crime”.
Said the Foyle MLA: ““On behalf of the SDLP, I want to extend our thoughts and prayers to Lyra McKee’s family this morning.
“They are experiencing the unthinkable loss of their daughter in the most heartbreaking circumstances.
“We have all lost an incredible young talent.
“I had the opportunity to speak with Lyra on a number of occasions as a journalist, as will politicians and leaders from all parties and communities.
“She had a passionate thirst for the truth and for telling the stories of people who had been forgotten or abandoned.
“Her character and values stand in stark contrast to the cowards who fired indiscriminately at police officers in Derry last night and have murdered a young woman who had so much to contribute to shaping our society and bringing people together.
“This news, coming on Good Friday, is a dark reminder to us all that our peace is fragile and that we must protect it everyday from those who want to shatter the progress that we have made.
“Those responsible for this heinous crime need to be faced down, they need to be made to realise that their fight is not with the PSNI or with young journalists doing their job.
“Their fight is with all of us, the people of Ireland. And it is a fight that they will never win.
“Today our thoughts are with Lyra’s family and friends. We should all remember her passion, humour and thirst for justice.”
Sinn Féin’s vice-president Michelle O’Neill said she was “shocked and saddened at the tragic news”.
She added: “I unreservedly condemn those responsible for killing this young woman.”
DUP leader Arlene Foster tweeted: “Heartbreaking news.
“A senseless act. A family has been torn apart.”
The SDLP’s Foyle MLA Mark H Durkan tweeted: “Just leaving Creggan, heartbroken and angry at the senseless loss of a young life.
“Violence only creates victims, that’s all it ever has done.
“The thoughts and prayers of our city are with the young woman’s family and friends, may she rest in peace.”