As part of my relocation package, my employer shall reimburse closing costs and 6% brokers fee for the sale of my home. The fees were reimbursed & counted towards my income so tax was deducted automatically. The income they paid me was used to pay the broker fees. Can I deduct this from my income?

I think so, as part of your moving expenses on Form 3903.

Many relocation packages gross up the reimbursement to cover taxes. But either way you can claim the expenses to offset the income.