Linnett made 72 appearances in all competitions for Birmingham in four seasons with the club.
The 23-year-old former Leicester trainee joined Blues in 2013 after three years with Arsenal.
"We believe she has the potential to flourish and become a top international striker," manager Rick Passmoor said.
Notts County Ladies have signed striker Kirsty Linnett after she turned down a new contract with Women's Super League One rivals Birmingham City.