Ken, who is currently living in Florida, is on a dialysis machine and will get his second kidney transplant. The first came in 1991 from an organ donor. But that kidney, which is 70-plus years old, is failing.
Rick is expected to be in the hospital for two days, while Ken will be hospitalized for at least five days.
"I am ecstatic. I'm very blessed and honored," Ken said about getting the kidney from his brother. "This really alleviates so much stress in my life. I know that everything is going to be great."
Rick said it was an emotional moment when he learned that he was a match for his brother.
"It means my brother will be able to live -- and that is exciting," Rick said.
Rick informed general manager Mike Rizzo and manager Jim Riggleman of his decision on Thursday -- and both gave Eckstein their support. Rick is hoping to go back to teaching the fundamentals of hitting to professional ballplayers within a week.
"As far as Rick is concerned, it's a no-brainer. It needs to be done," Riggleman said. "He is a match for his brother. With what's going on with his family, it's something they have to watch closely."
Kidney disease runs in the Eckstein family. Father Whitey and sisters Christine and Susan have all had kidney transplants. All three are doing fine. Christine is currently helping Ken go through his ordeal.
Rick and his younger brother, free-agent infielder David Eckstein, have been spared from similar problems.
Asked how he has stayed strong throughout his family's misfortunes, Rick said, "You handle what you are dealt. My glass is overflowing -- every day is a blessing. You do what you need to do. Looking at what my family has gone through, my gosh, they are tougher than I can ever dream of [being], based on the things they have gone through in their lives.
"I look at everything and try to see the positives. That's the way my mind works. Now, we are moving on to a stage where the kidney is going to recapture a quality of life that Ken hasn't had, and that's exciting. I'm going to be fine."
Before going through the procedure, Rick and Ken would like to make the public aware of the importance of being an organ donor. They said it has had a positive impact on their family. It was their mother, Patricia, who donated her kidney to Susan. Family friends have also given kidneys to Whitey and Susan. A family friend gave Whitey a kidney, while Christine received hers from a donor who passed away.
"I would love to have a cure, but I think the first step is getting the word out about organ donations," Ken said. "My sister gave me a statistic that 12 people are added to the national donors list every day -- and 18 die every day. There are a million people on the list. So my first thing is, if everyone could give a kidney, we wouldn't have a list."
Bill Ladson is a reporter for MLB.com and writes an MLBlog, All Nats All the time. He also could be found on Twitter @WashingNats. This story was not subject to the approval of Major League Baseball or its clubs.