Yes, its a straight bolt on.
Since the combustion chambers on the 351 heads are larger than the chambers on the 289......the compression will  be very low using the 351 heads.
If you plan to super charge the engine the compression will be fine but......if you don't then the heads need to be machined(milled) down. Unless the 351 heads are in "excellent" condition...after market heads could cost about the same.
IF the 289 heads are not damaged...why not just use them?   Stronger camshaft.......hi-rise intake with bigger carburetor ....headers  could get you close to 325 hp. 
The valve springs, retainers, etc. will need to be change with either heads for the camshaft to perform correctly.
Better gear ratio in the differential will be needed to get the performance you want....using  a high performance camshaft and better breathing.
Can you do any of the work yourself?
Welcome to the board BTW
6sally6

I was going to mention also that the intake manifold gaskets might be different depending on the year of the heads because of the shape of the coolant passage in the heads. Other than that the heads should bolt right on. Another thing to be mindful of is style of rocker arms, I think the 289's and the 69 351 heads will use stud mount rockers some of the newer stuff is bolt down rocker assemblies and just make sure the rocker studs are the same diameter between the 289's and 351W heads or you will be buying different rocker arms also.

Be sure to get the correct FORD head gasket to match the water ports...we just put a set of 351W heads on a 260...with 3 twos...

Water passages between the head and block are the same. so no problem with head gaskets.  Intake gaskets MUST be for a 69 351W as the port is shaped a little different.  See the article on the MustangSteve site on how to install an intake manifold. https://www.mustangsteve.com/intake.html  It shows the port differences.

Use flat top pistons for sure as 6sally6 said - 69 351W heads have 60cc combustion chambers, which is same as if you installed Edelbrock heads having 60cc chambers.

If you use the 69 heads, be sure to install screw-in type rocker studs.  The pressed in studs are prone to pulling out.

Don't expect much HP increase unless you also bump up compression and do some porting on the heads.  They are better flowing than 289 or 302, but the compression decrease can easily offset any flow increase.

I'm pretty sure there were differences between the steam holes in the 289 and 302 blocks, so I assumed that carried over to the 351 blocks.  Relatedly, when I put GT 40P heads on my 302 I had to plug the steam holes in the block and drill new ones to match those in the heads.

MS wrote:

Water passages between the head and block are the same. so no problem with head gaskets.  Intake gaskets MUST be for a 69 351W as the port is shaped a little different.  See the article on the MustangSteve site on how to install an intake manifold. https://www.mustangsteve.com/intake.html  It shows the port differences.

Use flat top pistons for sure as 6sally6 said - 69 351W heads have 60cc combustion chambers, which is same as if you installed Edelbrock heads having 60cc chambers.

If you use the 69 heads, be sure to install screw-in type rocker studs.  The pressed in studs are prone to pulling out.

Don't expect much HP increase unless you also bump up compression and do some porting on the heads.  They are better flowing than 289 or 302, but the compression decrease can easily offset any flow increase.

6sally6 wrote:

A crate motor may indeed be a more simply approach to your situation.  Without a good supply of swap meet parts you  would be hard pressed to "build-one-cheaper".
Be sure and check Summit's prices on crate motors. I have found they are usually less expensive on almost everything automotive. Great selection too.  Also look at Skip White's selection of crate motors and prices. I have no personal experience with Skip White(other than an alternator) but have read several reports on the internet of  satisfied customers.
Yes............if I were in Belgium ...I would opt for the crate engine option.
6sally6

Very wise recommendation....I second the motion....jj

MS wrote:

Beware of crate motors filled with the latest Chinese version of your favorite parts.  I prefer to build my own so I know exactly what I have.
Now, I know I have a busted lifter ! 

I agree with getting a crate motor.  However, get one from a very responsible/quality builder like Ford Racing or Edelbrock.  a 331 cu in would be my recommendation- more longivity.  350hp is easy and all of your 289 brackets, etc will fit.

​You can use your existing oil pan, too.  351's require a different pan that may not fit your car if it did not come from a Mustang.