The tourists' number three batsman has endured an ongoing battle with the illness for some time and is to take a break from cricket for the "foreseeable future".
Trott, 32, made just 19 runs in the first Ashes Test at the Gabba as he twice fell cheaply to Mitchell Johnson.
His batting was subsequently described as "poor" and "weak" by Australia opener David Warner, who has been branded "gobby" by former England batsman Geoffrey Boycott.
Hugh Morris, managing director of England cricket, said: "The cricket side of things is unimportant now, all that matters is that Jonathan is given the time, support and space he needs to recover.
"The ECB will provide all the assistance we can to help Jonathan and his family through this period. Jonathan has asked for privacy while he recovers, and I would urge everyone to respect that."
Trott himself said: "I don't feel it is right that I'm playing knowing that I'm not 100 per cent and I cannot currently operate on the level that I have done in the past.
"My priority now is to take a break from cricket so that I can focus on my recovery. I want to wish my team-mates all the very best for the remainder of the tour."
England have no plans at this stage to replace Trott in their squad.
The situation is similar to Marcus Trescothick's Ashes experience in 2006, when he flew home following two tour matches, citing a "recurrence of a stress-related illness".
Trescothick later confirmed he was diagnosed as clinically depressed, and he never played for England again.
Michael Yardy also returned home from the World Cup in 2011 after suffering from depression.
for stress read depression - a silent killer that needs to be taken more seriously by all of us. Hope Trott gets proper help— Kevin Garside (@GARSIDEK) November 25, 2013
Sad news, hope trotty is ok.— Marcus Trescothick (@Trescricket) November 25, 2013