Jake Brewer, 34, died while taking part in the 150-mile Ride to Conquer Cancer event on Saturday.
The senior policy advisor in the chief technology office lost control of his bike and was hit by a vehicle.
Mr Obama said: “Jake devoted his life to empowering people and making government work better for them.”
He said Mr Brewer had “a brilliant mind, a big heart, and an insatiable desire to give back”.
“He worked to give citizens a louder voice in our society. He engaged our striving immigrants. He pushed for more transparency in our democracy. And he sought to expand opportunity for all.
Mr Brewer, from Alexandria, Virginia, reportedly lost control of his bike on a sharp curve in Howard County, Maryland.
Earlier in his career Mr Brewer led global policy and external affairs at Change.org, the online petition website.
He also worked on a number of initiatives with the aim of using technology to improve people’s lives and was part of the Obama administration’s efforts to expand broadband connectivity.
“I will miss him forever, even more than I can know right now,” she wrote.
“I will strive and pray not to feel I was cheated of many years with him, but cherish the gift of the years I had. In a life where nothing is guaranteed, Jake made the absolute, ever-lovin’ most of his time with all of us.”
The president said he and his wife would be praying for the Brewer family, adding: “They’ll always have a family here at the White House.”