Consider a company with value of $1000, with 100 shares outstanding. Each share is $10. Buying back 10 shares, the company spent $100, so the company is now worth $900 and has 90 shares outstanding. Each share is still $10.
This is the basic model that shows share price should be unaffected by buybacks, but there are other effects. The buyback could signal to investors that the company is unlikely to be inefficient with capital, so investors would value the company at $910 instead of $900.
Alternatively, in a demand/supply model of shares, the buybacks could have exhausted some of the supply of shares, so the valuation for the company settled on by the rest of the market is higher.
There's no clear answer here, but reality is probably somewhere between these models.