Depending on a placement of your chimney (exterior with one wall attached to the house) or interior chimney (only upper section exposed above the roof / running through the attic) there are a couple of ways to deal with it.
I don’t know what the mortar condition is between the bricks but if there are any gaps it could allow rain water penetration resulting in leakage and further chimney deterioration – tuckpointing should be considered if this is the case.
To prevent or at least minimize possibility of condensation and leakage from the base of your chimney its bottom portion needs to be insulated before you seal it off. This is to prevent any warm air and moisture from your house from getting into the chimney stack and forming condensation on its walls (eventually leaking back through the base of the chimney).
For an exterior type chimney I would suggest to fill with insulation entire section that is between the interior and exterior (in most case this will be the house wall thickness). Some chimneys are partially underground (outside the house foundation) and if there are any leaks in that underground part it might be necessary to dig around it to stop ground water / moisture from penetrating walls (there will be no more heat to accelerate evaporation) or / and fill that entire underground section with insulation or some solid material. Drainage tubing is also an option but if it’s leaking don’t put any insulation below the vent opening.
If it is completely outside and above ground, just fill-in with insulating material the thickness of the chimney / house wall (expanding foam will do the job).
If you want the process to be reversible, maybe to use the existing chimney for a wood stove or a fireplace in the future (you would need a liner), you can use fiberglass blanket; just make a tight roll and push it through the old furnace vent pipe opening and let it expand). If it’s a tight fit, blown in type fiberglass might be a better choice.
For capping the bottom I’d use expanding foam insulation as a final seal (up to the chimney wall thickness), mortar to seal the opening tight, or a metal cap. If you have a cleanout at the base of the chimney, seal it air tight as well.
Have the top of your chimney finished with a crown and a screened rain cap to stop water penetration and rodents / birds from getting in. I wouldn’t seal the top air-tight because it is a brick chimney and brick / mortar absorb water so whatever moisture gets inside the chimney has to evaporate somewhere / somehow. Otherwise it will flow down the chimney walls.
For the interior chimney, seal the bottom opening same way as above; mortar / expanding foam / rolled insulation and a metal cap. You can even wrap the exposed chimney walls (it might be the entire height of a basement) with a blanket insulation to minimize heat transfer. Finish the top the same way as well.
The only problem with an interior brick chimney is if it runs through a poorly ventilated attic (which would make it warmer than exterior air temperature during the winter), or if parts of it are exposed to conditioned / warm air from the house. When it gets very cold and you start noticing moisture around the base of your chimney (basement?) you’ll have to look for ways of isolating the chimney walls from any heat sources and / or making your attic as cold as exterior / improve attic ventilation.