I actually did this first in a vacation home replacing very similar Honeywell thermostats.
My first attempt used this
Aube Technologies RC840T-120 Electromechanical Relay with Built In Relay
(Too much of a noobie to post links - these are available on Amazon)
But that didnt provide enough power for the Ecobee. So I switched to this
Aube Technologies 300612 RC840 On/Off Switching Electric Heating Relay
With an external 24v transformer (Aprilaire 4010)
Fortunately I had space around the breaker box. At the original thermostat position I just bypassed it. And then back at the breaker box I removed the wiring from the breaker and connected to the output of this relay and then ran a new wire from the breaker to the input of this relay.
On the low voltage side this plus the 24v to the Ecobee (only 3 wires needed). And then because the Ecobee was close to the breaker and not the original thermostat I used the Ecobee remote sensors mounted on the cover plate of where the original thermostat was to get a more accurate reading and motion sensing.
Hope that helps!