We know this because he wrote about it in his journal on March 8, 1855:
This morning I got my boat out of the cellar and turned it up in the yard to let the seams open before I calk it. The blue river, now almost completely open (i.e., excepting a little ice in the recesses of the shores and a good deal over the meadows), admonishes me to be swift.
We seemed to be embarked on the placid current of our dreams, floating from the past to future as silently as one awakes to fresh morning or evening thoughts. We glided noiselessly down the stream, he wrote.
Three years later, John died in Henry's arms. He had developed tetanus after cutting himself shaving.
From 1845-47, Henry David Thoreau lived at Walden Pond, where he wrote A Week on the Concord and Merrimack Rivers as a tribute to his brother. In it, he described the Concord River and the grassy meadows through which it flowed:
The Musketaquid, or Grass-ground River, though probably as old as the Nile or Euphrates, did not begin to have a place in civilized history, until the fame of its grassy meadows and its fish attracted settlers out of England in 1635, when it received the other but kindred name of CONCORD from the first plantation on its banks, which appears to have been commenced in a spirit of peace and harmony. It will be Grass-ground River as long as grass grows and water runs here; it will be Concord River only while men lead peaceable lives on its banks. ...Concord River is remarkable for the gentleness of its current, which is scarcely perceptible, and some have referred to its influence the proverbial moderation of the inhabitants of Concord ... it appears to have been properly named Musketaquid, or Meadow River, by the Indians. For the most part, it creeps through broad meadows...