output with awk:
$ awk 'NR==FNR {a[$1,$2];next} ($1,$2) in a' file1.txt file2.txt
or
$ awk 'NR==FNR {a[$1,$2]++;next}a[$1,$2]' file1.txt file2.txt
Chr01 45965 SNP G C 26.33 100.00 6 21 6
output with grep (with OP text):
$ grep -wf file1.txt file2.txt
Chr01 45965 SNP G C 26.33 100.00 6 21 6
output with tsv-utils:
$ tsv-join -f file2.txt --key-fields 1,2 file1.txt --append-fields 3-10
Chr01 45965 SNP G C 26.33 100.00 6 21 6
Input:
$ tail -n+1 file1.txt file2.txt
==> file1.txt <==
Chromosome Position
Chr01 45943
Chr01 45965
Chr01 45981
Chr01 46122
Chr02 45965
==> file2.txt <==
Chr01 6789 SNP A T 15.17 90.91 6 18 6
Chr01 6795 SNP G T 12.11 81.82 6 17 4
Chr01 45965 SNP G C 26.33 100.00 6 21 6
Chr01 459656 SNP G C 26.33 100.00 6 21 6
Chr01 4596111111111 SNP G C 26.33 100.00 6 21 6