Ms Garraway announced the death of her husband, an author and former political advisor, on Friday. He had been living with serious complications from coronavirus since March 2020.
The TV presenter said messages of support "really does mean so much" as she appeared on Good Morning Britain via video message.
Ms Garraway said: "I'm so lucky to feel connected to you all through these messages at this time when the raw pain of grief can be so isolating.
"I am certain that it is the support that you have given me and sent to Derek that has sustained us through these tough nearly four years, motivating us to fight on for each other and for those who can't fight for themselves and it will sustain us to continue that fight in the weeks and months and years to come.
"I look forward to waking up with you very soon again on Good Morning Britain to celebrate life in all its wonder and challenge again."
The GMB star continued: "I hope you forgive me for taking some time to be at home. My family is so grateful that we could be with our dearest Derek in his final moments - something not all get to share.
"Maybe you too are going through grief yourself or have done in the past. I send love and support for you too.
"We are taking time to heal ourselves now that Darcey and Billy know their daddy is at peace and free from pain and struggle. I shall be thinking of you all until we are reunited very soon.
"In the meantime, hug your loved ones close. All my love, Kate."
Among those sending messages of condolences on Friday were Garraway’s Good Morning Britain co-hosts, Susannah Reid and Charlotte Hawkins, who commented: “So desperately sorry Kate, it’s absolutely heart-breaking. So much love to you all.”
Elton John said: “So sorry to hear of this news, Kate. Love and thoughts to you and your family.”
Former British Prime Minister Tony Blair, with whom Draper worked in the 1990’s, said: “It is extraordinary and remarkable that Derek survived so long after the ravages of COVID. And that was in large measure due to the love Derek had for his family and they for him. This also says something very special about Derek.
“He was a tough sometimes ruthless political operative, a brilliant adviser and someone you always wanted on your side. But underneath that tough exterior he was a loving, kind, generous and good natured man you wanted as a friend,” Blair continued.
“He was an important part of the New Labour story, at the centre of things right at the beginning. But most important of all, he was a good colleague and great friend. And we will miss him deeply.”
Ms Garraway is taking an indefinite leave of absence from TV and radio work.
The pair married in 2005 and had two children, Billy and Darcey.
