The 29-year-old admitted the last few days had been "extremely hard, scary, and disappointing" after it was confirmed she had received treatment on Monday for a haematoma, suffered as a result of a pulmonary embolism which was diagnosed last week.
"Thank you everyone for all of your prayers, concerns, and support," the former world No 1 said in a statement.
"This has been extremely hard, scary, and disappointing. I am doing better, I'm at home now and working with my doctors to keep everything under control.
"I know I will be OK but am praying and hoping this will all be behind me soon.
"While I can't make any promises now on my return, I hope to be back by early summer. That said, my main goal is to make sure I get there safely."
A separate statement released yesterday confirmed the 13-time grand slam winner would spend the immediate future under close medical scrutiny.
"Serena did indeed suffer from a pulmonary embolism last week, and the haematoma was another unexpected scare that was subsequently removed. Thankfully everything was caught in time," the statement read.
"With continued doctor visits to monitor her situation, she is recuperating at home under strict medical supervision."
The Women's Tennis Association expressed relief that the worst appears to be over for Williams, saying in a statement: "We are very heartened to hear that despite the serious medical situation that she had to deal with, Serena is now recovering and on the road to full health and a possible return to professional tennis in early summer.
"Serena is a champion on and off the court, and we, along with her millions of fans around the world, wish her a speedy recovery."
Williams has been out of competitive action since winning Wimbledon in July. She subsequently cut her foot on some broken glass, an injury which has required two operations.
Despite her lengthy absence, she is still ranked 11th in the world.
On Sunday night, the day before her reported emergency treatment at Cedars-Sinai Medical Center, she attended the Elton John Aids Foundation Academy Awards Viewing Party in Los Angeles.