The World Cup winner, 80, was admitted to hospital on 7 April.
Tottenham said their record goalscorer, who had a severe stroke in 2015, had “not tested positive for Covid-19 nor suffered another stroke”.
A statement on Greaves’ official Facebook page said he was “back at home recuperating with his wife Irene”.
It added: “He has been very ill and we are hoping he will be fine going forward.”
Greaves, who scored 266 league and cup goals for Spurs, began his career at Chelsea and also had spells at West Ham and AC Milan.
He holds the record for most top-flight goals in English football, with a total of 357.
He is fourth on the list of all-time England goalscorers, behind Wayne Rooney (53), Sir Bobby Charlton (49) and Gary Lineker (48).
“If and when there is any more news we will let you all know,” the statement added. “Thanks to the thousands of you that have sent goodwill messages.
“We love that so many of you still hold Jimmy so dear to your hearts and it’s lovely to know that there is still so much love for him in the world.”